Dipartimento di Matematica e Informatica 'Ulisse Dini'

Recapiti

0552751462

luca.avena(AT)unifi.it

Luca AVENA

Orario di ricevimento (aggiornato al 19/10/2023)

Disponibile su appuntamento previa richiesta tramite email.

Luca AVENA

Curriculum

1. Academic positions

Date: 01/09/2023-present Position: Associate Professor, Institution: University of Florence, DIMAI, Italy.

Date: from 01/03/2021-31/08/2023, Position: Associate Professor (UHD), Institution: University of Leiden, MI, The Netherlands.

Date: 15/10/2019-14/10/2021 & 15/11/2023-14/11/2025, Position: Visiting Professorship in “Mathematical theory of Complex Networks”, Institution: IMT School for Advanced Studies Lucca, Lucca, Italy.

Date: 01/06/2020-28/02/2021 Position: Assistant Professor (UD), Institution: University of Leiden, MI, The Netherlands.

Date: 01/06/2014-31/05/2020, Position: Assistant Professor (Tenure Track), funded by the NWO Gravitation Program NETWORKS, Institution: University of Leiden, MI, The Netherlands.

Date: 01/04/2013-31/05/2014, Position: Post-doc in the group of Prof. Dr. Wolfgang König, Institution: Weierstrass Institute (WIAS), Berlin, Germany.

Date: 01/11/2010-31/03/2013, Position: Post-doc in the group of Prof. Dr. Erwin Bolthausen, Institution: Department of Mathematics, University of Zürich, Switzerland.

2. Academic education

PhD in Mathematics Institution:Leiden University, Period:2006-2010, Date of PhD award:26/10/2010, Supervisor:Prof. Dr. Frank den Hollander, Thesis title: Random Walks in Dynamic Random Environments.

Master’s degree in Mathematics (cum laude) Institution:Università di Roma ROMATRE, Date:July2006, Supervisor:Prof. Dr. Fabio Martinelli, Thesis title: On the threshold of the random k-sat.

Bachelor’s degree in Mathematics Institution:Università di Roma ROMATRE, Date:July2004.

Erasmus student Institution:Universidad de Granada, Spain, Date:2002-2003.

3. Academic Teaching

ASN Italian habilitation Abilitazione Scientifica Nazionale, both as Full Professor (I fascia) and as Associate Professor (II fascia) for 01/A3 Analisi Matematica, Probabilità e Statistica Matematica. Obtained on February 6,2023, from MIUR (Ministero dell’ Istruzione e del Merito), Italy,https://abilitazione.miur.it/public/pubblicarisultati_2021.php.

BKO Dutch habilitation Basis Kwalificatie Onderwijs, Leiden, The Netherlands. Obtained on October24,2017.

Instructor, Florence University:

Course title:Calcolo delle Probabilità. Period: Fall2023. Given jointly with G. Bet. Course for bachelor students in mathematics.

Course title:Analisi Matematica II & Probabilità. Period: Fall2023. Given jointly with G. Giovannardi and I. Lucardesi. Course for master students in engineering (ingegneria informatica).

Instructor, Leiden University:

Course title: Complex Networks. Period: Fall 2022. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Markov chains and applications. Period: Fall 2022. Course for master students in mathematics.

Course title: Stochastic Processes. Period: Spring 2022. Given jointly with F. den Hollander and G. Bonnet within the national program MASTERMATH.

Course title: Complex Networks. Period: Fall 2021. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Markov chains and applications. Period: Fall 2021. Course for master students in mathematics.

Course title: Interacting Particle Systems. Period: Fall 2020. Within the national program MASTERMATH.

Course title: Complex Networks. Period: Fall 2020. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Introduction to Probability Theory (Inleiding Kansrekening). Period: Spring 2020.

Course title: Complex Networks. Period: Fall 2019. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Probability Seminar: Stories from Asymptopia. Period: Fall 2019. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Course title: Introduction to Probability Theory (Inleiding Kansrekening). Period: Spring 2019. Course for bachelor students in mathematics.

Course title: Stochastic Models for Genetic Evolution. Period: Spring 2019. Given jointly with F. den Hollander. Course for master students in mathematics.

Course title: Probability Seminar: Random Graph Ensembles. Period: Fall 2018. Given jointly with F. den Hollander. Course for master students in mathematics.

Course title: Introduction to Probability Theory (Inleiding Kansrekening). Period: Spring 2018. Course for bachelor students in mathematics.

Course title: Introduction to Stochastic Processes. Period: Spring 2018. Given jointly with F. Spieksma within the national program MASTERMATH.

Course title: Probability Seminar: Random Walks in Random Environments. Period: Fall 2017. Given jointly with F. den Hollander. Course for master students in mathematics.

Course title: Stochastic Models for Genetic Evolution. Period: Spring 2017. Course for master students in mathematics.

Course title: Probability Seminar: Large Deviations & Applications. Period: Fall 2016. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Course title: Random Walks, Period: Fall 2016. Course for bachelor and master students in mathematics.

Course title: Coupling Theory. Period: Spring 2016. Course for master students in mathematics.

Course title: Random Walks. Period: Fall 2015. Course for bachelor and master students in mathematics.

Course title: Probability Seminar: Random Matrix Theory. Period: Fall 2015. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Course title: Stochastic Models for Genetic Evolution. Period: Spring 2015. Course for master students in mathematics.

Course title: Probability Seminar: Large Deviations & Applications. Period: Fall 2014. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Teaching Assistant:

(Zürich University) Logic, Fall 2012, Instructor: L. Halbeisen (Department of Mathematics, Zürich University);

(Zürich University) Probability Theory, Spring 2012, Instructor: J. Najnudel ;

(Zürich University) Probability Theory, Spring 2011, Instructor: J. Najnudel ;

(Leiden University) Statistiek voor LST, Spring 2010, Instructor: R.J. Kooman ;

(Leiden University) Wiskunde 2 voor LST, Spring 2009, Instructor: R.J. Kooman;

(Leiden University) Maat en Integratietheorie, Fall 2008, Instructor: F. Redig;

(Leiden University) Applied Analysis, Fall 2007, Instructor: V. Rottschäfer.

(ROMATRE University) Probability Theory 1 (CP1), Spring 2006, Instructor: F. Martinelli;

(ROMATRE University) Probability Theory 1 (CP1), Spring 2005, Instructor: F. Martinelli.

4. Academic Supervisions

PostDoc:

Rangel Baldasso, MI, Leiden. Topic: Contact process and voter model on random graphs. Period: May 2020- May 2023.

Matteo Quattropani, MI, Leiden. Topic: Metastability for interacting particle systems on random graphs. Period: Sept. 2021-Aug. 2022.

Conrado da Costa, MI, Leiden. Topic: Random motion in random environments. Period: Sept. 2016-Sept.2019.

Yuki Chino, MI, Leiden. Topic: Random walks in cooling random environments. Co-supervisor: F. den Hollander. Period: Sept. 2017-Sept. 2019

PhD:

Nandan Malhotra, MI, Leiden. Topic: spectra of random graph ensembles. Co-supervisor: R. Hazra. Start: September 1, 2021.

Federico Capannoli, MI, Leiden. Topic: voter model on random graphs. Co-supervisor: R. Hazra. Start: September 1, 2021.

Margherita Lalli, PhD candidate at IMT, Lucca, under the supervison of D. Garlaschelli. One year internship in Leiden under my supervision within the Erasmus+ programme. Topic: Spectral properties of random graphs. Period: April 2021/August 2022.

Twan Koperberg, MI, Leiden. Topic: Random rooted forests and exploration of sparse networks. Co-supervisor: A. Gaudilliere. Start: March 1, 2020.

Oliver Nagy, MI, Leiden. Topic: Random walks on dynamic random graphs. Co-supervisors: F. den Hollander and R. van der Hofstad. Start: February 1, 2020.

Hakan Guldas, MI, Leiden. Thesis title: ``Random walks on dynamic random graphs”. Co-supervisors: F. den Hollander and R. van der Hofstad. Defended on July 3, 2019.

Master:

Niels Kolebrander, MI, Leiden. Thesis title: "Statistical properties for a class of random billiards''. Co-supervisor: D. Terhesiu (2023).

Irina Gurewitsch, MI, Leiden. Thesis title: ``Using random rooted spanning forest for network immunization''. Co-supervisor: M. Emmerich (2022).

Vittorio Magrini, MI, Leiden. Thesis title: ``Local limits of random rooted spanning trees and forests on dense geometries" Co-supervisor: C. da Costa (2020).

Bruno Stordeur, Universite d'Aix-Marseille, Marseille, one month internship in Leiden as part of his master project, topic: Wavelets for signals on graphs. Co-supervisors: Fa. Castell and C. Melot (June 2019).

Adi Kiang, MI, Leiden. Thesis title: ``Networks coarse-graining through intertwining dualities”. Co-supervisor: F. den Hollander (2019).

Khadija Lachhab, MI, Leidem. Thesis title: ``Wright-Fisher model with seed bank and selection”. Co-supervisor: F. den Hollander (2019).

Thomas van Hees, MI, Leiden. Thesis topic: Networks filtering through discrete curvatures. Co-supervisor: D. Garlaschelli (2018).

Alvin Peters, MI, Leiden. Thesis title: ``Electrical networks and Markov chains: Classical results and beyond”. Co-supervisor: S. Taati (2016).

Matteo Quattropani, MI, Leiden. Thesis title: ``Spectral techniques of Community Detection: a probabilistic perspective”. Co-supervisor: D. Garlaschelli (2016).

Bachelor:

Giovanni Pepe, DIMAI, Firenze. Topic ``Semicircle law and spectra of random graphs'', co-supervisor: G. Bet (2024).

Bob Vermulen, MI, Leiden. Thesis title: ``Local convergence of random graphs'', co-supervisor: R. Baldasso (2022).

Jochem Boelema, MI, Leiden. Thesis title: ``Introduction to renormalization techniques in percolation theory'', co-supervisor: R. Baldasso (2021).

Niels Kolebrander, MI, Leiden. Thesis title: ``Billiards, random walks and gases: some case studies'', co-supervisor: D. Terhesiu (2021).

Jannetje Driessen, MI, Leiden. Thesis title: ``Loop-Erased Partitions on Tree Structures" (2019).

Twan Koperberg, MI, Leiden. Thesis title: ``Couplings and Matching: On the equivalence of Strassen's theorem and some combinatorial theorems'', co-supervisor: S. Taati (2016)

5. Research Production

Pubblications:

L. Avena and C. da Costa, Laws of large numbers for weighted sums of independent random variables: a game of mass, Journal of Theoretical Probability, https://doi.org/10.1007/s10959-023-01296-z (2023).

L. Avena, H. Guldas, R. van der Hofstad, F. den Hollander and O. Nagy, Linking the mixing times of random walks on static and dynamic random graphs, Stochastic Processes and their Applications 153, 145-182 (2022).

L. Avena, A. Gaudilliere, P. Milanesi and M. Quattropani, Loop-erased partitioning of a graph: mean-field analysis, Electronic Journal of Probability 27 (67), 1-35 (2022).

L. Avena, Y. Chino, C. da Costa and F. den Hollander, Random walk in cooling random environment: recurrence versus transience and mixed fluctuations, Annals de l’Institut Henri Poincare, Probability and Statistics 58 (2), 967-1009 (2022).

L. Avena, F. Castell, A. Gaudilliere, and C. Melot, Approximate and exact solutions of intertwining equations through random spanning forests, In and Out of Equilibrium 3. Celebrating Vladas Sidoravicius, Progress in Probability 77, Springer (2021).

L. Avena, F. Castell, A. Gaudilliere and C. Melot, Intertwining wavelets or multiresolution analysis on graphs through random forests, Applied and Computational Harmonic Analysis 48 (3), 949-992 (2020).

L. Avena, O. Gun and M. Hesse, The parabolic Anderson model on the hypercube, Stochastic Processes and their Applications} 130 (6), 3369-3393 (2020).

L. Avena, H. Guldas, R. van der Hofstad and F. den Hollander, Random walks on dynamic configuration models: a trichotomy, Stochastic Processes and their Applications 129 (9), 3360-3375 (2019).

L. Avena and F. den Hollander, Random walks in cooling random environments, Sojourns in Probability Theory and Statistical Physics–III, A Festschrift for Charles M. Newman, Springer, Proceedings in Mathematics & Statistics series}, Vol. 300, 23-42 (2019).

S. Barthelme, N. Tremblay, A. Gaudilliere, L. Avena and P.-O. Amblard, Estimating the inverse trace using random forests on graphs, Proceedings GRETSI Symposium on Signal and Image Processing, Lille, France (2019). Available on ArXiv:1905.02086 (2019).

L. Avena, Y. Chino, C. da Costa and F. den Hollander, Random walk in cooling random environment: ergodic limit and concentration inequalities, Electronic Journal of Probability 24(38), 1-35 (2019).

L. Avena, F. Castell, A. Gaudilliere and C. Melot, Random forests and networks analysis, Journal of Statistical Physics 173(3-4), 985-1027 (2018).

L. Avena, H. Guldas, R. van der Hofstad and F. den Hollander, Mixing times of random walks on dynamic configuration models, Annals of Applied Probability 28(4), 1977-2002 (2018).

L. Avena and A. Gaudilliere, A proof of the transfer-current theorem in absence of reversibility, Statistics and Probability Letters 142, 17-22 (2018).

L. Avena, M. Jara and F. Vollering, Explicit LDP for a slowed RW driven by a symmetric exclusion process, Probability Theory and Related Fields 171(3-4), 865-915 (2018).

L. Avena, O. Blondel and A. Faggionato, Analysis of random walks in dynamic random environments via L2- perturbations, Stochastic Processes and their Applications 128(10), 3490-3530 (2018).

L. Avena and A. Gaudilliere, Two applications of random spanning forests, Journal of Theoretical Probability 31(4), 1975-2004 (2018).

L. Avena, O. Blondel and A. Faggionato, A class of random walks in reversible dynamic environments: antisymmetry and applications to the east model, Journal of Statistical Physics 165, 1-23 (2016).

L. Avena, E. Bolthausen and C. Ritzmann, A local CLT for convolution equations with an application to weakly self-avoiding random walks, Annals of Probability 44 (1), 206-234 (2016).

L. Avena, T. Franco, M. Jara and F. Vollering, Symmetric exclusion as a random environment: hydrodynamic limits, Annals de l’Institut Henri Poincare, Probability and Statistics 51 (3), 901-916 (2015).

L. Avena, R. dos Santos and F. Vollering, Transient random walk in symmetric exclusion: limit theorems and an Einstein relation, ALEA, Latin American Journal of Probability and Mathematical Statistics 10 (2), 693-709 (2013).

L. Avena, Symmetric exclusion as a model of non-elliptic dynamical random conductances, Electronic Communications in Probability 17 (44), 1-8 (2012).

L. Avena and P. Thomann, Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures, Journal of Statistical Physics 147, 1041-1067 (2012).

L. Avena, F. den Hollander and F. Redig, Law of large numbers for a class of random walks in dynamic random environments, Electronic Journal of Probability 16, 587-617 (2011).

L. Avena, F. den Hollander and F. Redig, Large deviation principle for one-dimensional random walk in dynamic random environment: attractive spin-flips and simple symmetric exclusion, Markov Processes and Related Fields 16, 139-168 (2010).

L. Avena, Random Walks in Dynamic Random Environments, Ph.D. thesis. Available on the online catalogue of the Leiden University Library: www.catalogus.leidenuniv.nl, Leiden (2010).

Preprints:

L. Avena, F. Capannoli, R. S. Hazra, M. Quattropani, Meeting, coalescence and consensus time on random directed graphs, ArXiv:2308.01832 (2023). To appear in Annals of Applied Probability.

L. Avena, D. Garlaschelli, R. S. Hazra, M. Lalli, Inhomogeneous random graphs with infinite-mean fitness variables, ArXiv:2212.08462 (2022). To appear in Journal of Applied Probability.

L. Avena, R. Baldasso, R. S. Hazra, F. den Hollander, M. Quattropani, Discordant edges for the voter model on regular random graphs, ArXiv:2209.01037 (2022). To appear in ALEA, Latin American Journal of Probability and Mathematical Statistics.

L. Avena, C. da Costa and J. Peterson, Gaussian, stable, tempered stable and mixed limit laws for random walks in cooling random environments, ArXiv:2108.08396 (2021). To appear in Annals de l’Institut Henri Poincare, Probability and Statistics

L. Avena, J. Driessen and T. Koperberg, Loop-erased partitioning of a network: monotonicities & analysis of cycle-free graphs, ArXiv:2103.14436 (2021).

L. Avena, C. da Costa and F. den Hollander, Stochastic models for genetic evolution, Lecture notes, Mathematisch Instituut, Universiteit Leiden. Available at https://websites.math.leidenuniv.nl/probability/lecturenotes/BioStoch.pdf (2019).

L. Avena, M. Heydenreich, F. den Hollander, E. Verbitskiy and W. van Zuijlen, Random walks, Lecture notes, Mathematisch Instituut, Universiteit Leiden. Available at https://websites.math.leidenuniv.nl/probability/lecturenotes/RandomWalks.pdf (2016).

L. Avena and A. Gaudilliere, Random spanning forests, Markov matrix spectra and well distributed points, ArXiv:1310.1723 (2013).

6 Events Organisation

Workshop ``The Lorentz Gas'', December 19-23, 2022, Lorentz Center, Leiden, The Netherlands.

Workshop ``Celebrating Francesca Romana Nardi: a life in probability, building communities across Europe'', July 18-22, 2022, Aula Magna, Florence, Italy.

13-th NETWORKS TRAINING WEEK, May 9-12, 2022, De Schildkamp, Asperen,The Netherlands. See https://www.thenetworkcenter.nl/Education/Training-Weeks/

ICM 2018 satellite conference ``Topics in Mathematical Physics'', session on ``Complex Networks'', July 26-31, 2018. Sao Paulo, Brazil.

Workshop ``Random structures on the brain'', December 4-8, 2017, Lorentz Center, Leiden, The Netherlands.

Workshop ``Community Detection & Networks Reconstruction'', September 19-22, 2017, EURANDOM, Eindhoven, The Netherlands.

Workshop ``Randomness and Graphs: Processes and Structures'', September 11-15, 2017, EURANDOM, Eindhoven, The Netherlands.

XVI YEP (Young European Probabilists) workshop ``Networks: Probability, Combinatorics and Algorithms'', September 04-08, 2017, EURANDOM, Eindhoven, The Netherlands.

Stochastic Activity Month ``Random Graphs and Complex Networks: models, algorithms and applications'', September 2017, EURANDOM, Eindhoven, The Netherlands.

Workshop ``New results and challenges with random walks in dynamic random environment'', 11-13 January, 2017, Bristol, UK.

XIII YEP (Young European Probabilists) workshop ``Large Deviations for Interacting Particle Systems and Partial Differential Equations'', March 7-11, 2016, EURANDOM, Eindhoven, The Netherlands.

Stochastic Activity Month ``Probability and Analysis'', March 2016, EURANDOM, Eindhoven, The Netherlands.

Workshop ``Random Motion in Random Media'', 30 March-2 April, 2015, EURANDOM, Eindhoven, The Netherlands.

Stochastic Activity Month ``Random Walk and Random Media'', 23 March-24 April, 2015, EURANDOM, Eindhoven, The Netherlands.

16th Rencontres Mathematiques de Rouen, June 18-20, 2014, Rouen, France.

7 Selected Invited Talks

-2023

Meetings of random walks & consensus dynamics on random directed graphs, 30 January 2024, ICTS-NETWORKS WORKSHOP “CHALLENGES IN NETWORKS”, ICTS, Bangalore, India.

Meetings of random walks & consensus dynamics on sparse random digraphs, 23 November 2023, IMT Lucca, Italy.

Walking with Frank in various changing landscapes, 29 September 2023, workshop“New frontiers in Probability", Leiden, The Netherlands.

Tempi di mescolamento per camminate aleatorie su reti dinamiche, 8 September 2023, XXII Congresso dell'Unione Matematica Italiana, UMI, invited session organised by Elisabetta Candellero and Dario Trevisan, Pisa, Italy.

Meetings of random walks and consensus in voter dynamics on sparse random digraphs, workshop“Random walks in Bath", 7 June 2023, Wolfson Amphitheater, Bath, UK.

A network randomized k-centrality measure & applications to node immunization, 24 February 2023,“Leiden Complex Networks Network (LCN2)" meeting, Faculty of Science, Leiden, The Netherlands.

Evolution of discordances in voter dynamics on random regular graphs, online, 12 January 2023, workshop“Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2023", Fukuoka, Japan.

-2022

A randomized k-centrality measure & applications to networks node immunization, 6 December 2022, Eindhoven SPOR Seminar, Eurandom, Eindhoven, The Netherlands.

Anomalous fluctuations for random walks in dynamic random environments with resetting, 30 June 2022, IMS Annual Meeting in Probability and Statistics, invited session organised by Jonathon Peterson, London, UK.

Evolution of discordances in voter dynamics on random regular graphs, 15 June 2022, “Third italian meeting on Probability and Mathematical Statistics", Bologna, Italy.

A randomized k-centrality measure & applications to networks node immunization, 7 June 2022, General Mathematics Colloquium, UvA, Amsterdam, The Netherlands.

A randomized k-centrality measure & applications to networks node immunization, 30 May 2022, workshop “A day on Random Graphs”, TOR VERGATA, University of Rome, Italy.

-2021

Node immunization in networks: a scalable searching algorithm based on random rooted forests, online, 1 June 2021, IMT Lucca, Italy.

Random walks in cooling random environments: a journey on the one-dimensional lattice, online, 17 May 2021. Mathematics Department, Universidad Federal de Rio de Janeiro, Brazil.

Explorations of networks through random rooted forests, online, 6 April 2021, NMC, Nederlands Mathematisch Congres, 2021, The Netherlands.

Node immunization in networks: a scalable searching algorithm based on random rooted forests, online, 26 February 2021, Mathematics Department, Universita' degli studi di Padova, Italy.

-2020

Node immunization in networks: a scalable searching algorithm based on random rooted forests, online, 14 October 2020, Mathematics Department, Universidad Federal de Bahia, Salvador, Brazil.

Mixing time for RW on dynamic configuration model, 15 January 2020, workshop “Spectra, Algorithms and Random Walks on Random Networks”, CIRM Marseille, France.

-2019

Mesoscopic explorations of graphs through random rooted forests, 27 November 2019, workshop “Brain networks and metastability”, IMT Lucca, Italy.

Renormalisation for graphs and signals on graphs via random walk kernels, 25 November 2019, workshop “Network coarse-graining”, IMT Lucca, Italy.

Explorations of networks through random spanning forests: theory and applications, 22 November 2019, AN “AUTUMN” DAY IN PROBABILITY AND STATISTICAL PHYSICS, Florence, Italy.

Multiscale analysis of network data sets via random walk kernels, 20 November 2019, University of Pisa, Italy.

Processing data sets on networks: rooted forests and other probabilistic tools, 16 July 2019, conference “Complex networks: from socio-economic systems to biology and brain'' , Lipari, Sicily, Italy.

Processing data sets on networks: random forests and other probabilistic tools, 18 June 2019, “Second italian meeting on Probability and Mathematical Statistics", Vietri sul Mare (Salerno), Italy.

Sinai walk in cooling random environment, 30 May 2019, ``Japanese-Dutch meeting", Lorentz Center, Leiden, The Netherlands.

Random walks in cooling random environments, 21 May 2019, Max Planck Institute, Leipzig, Germany.

Network data-sets: randomized decomposition through forests and some related tools, 15 April 2019, Lecture day on the occasion of Ravi Kumar's visit, TU Eindhoven, The Netherlands.

Mixing time on dynamic configuration model, 15 January 2019, mathematics and physics department, Roma tre University, Rome, Italy.

-2018

Loop-erased partitioning: two-point correlations on mean-field models, 12 December 2018, Groningen Stochastics Seminar, Groningen, The Netherlands.

Network coarse-graining, Markov intertwining and metastability without asymptotics, 27 July 2018, conference “Topics in Mathematical Physics", ICM 2018 satellite conference, Sao Paul, Brazil.

Data sets on networks: some probabilistic tools and a new wavelet transform, 24 July 2018, Facultad de Ingeniera, Buenos Aires, Argentina.

Network coarse-graining, Markov intertwining and metastability without asymptotics, 17 July 2018, workshop ``Geometry and scaling of random structures", CIMPA School and X Escuela Santala, ICM 2018 satellite workshop, Buenos Aires, Argentina.

Random walks in cooling random environments, 11 June 2018, 40th SPA (Stochastic Process and their Applications) conference, invited session organised by Marton Balasz, Gothenburg, Sweden.

Network coarse-graining, Markov intertwining and a framework for metastability without asymptotics, 9 June 2018, workshop “ISI-NETWORKS Day'', Lipsius building, Leiden, The Netherlands.

Random walks in cooling random environments, 30 May 2018, FRANCO-DUTCH YEP-workshop “Mathematical statistical mechanics, random graphs and related topics'' EURANDOM, Eindhoven, The Netherlands .

Some probabilistic tools to process data sets on networks, 9 May 2018, workshop ``Brainstorm Day, Complex Networks'', Lorentz Center, Leiden, The Netherlands.

-2017

Data sets on networks: some probabilistic tools, 13 December 2017, workshop “Network Models: Structure and Function'', Oberwolfach, Germany.% 11-16 December 2017.

Data sets on networks: some probabilistic tools, 28 November 2017, series of lectures “This week's discoveries", Faculty of Science, Leiden, The Netherlands.

Minicourse: Random walks, forests and network analysis, 30 October-3 November 2017, 5th NETWORKS TRAINING WEEK, De Schildkamp, Asperen, The Netherlands.

A taste of randomness and disorder for lunch, 5 April 2017, lunch lecture for De Leidsche Flesch student association, Leiden, The Netherlands.

RW kernels, spanning forests and multiscale analysis on graphs, 1 March 2017, “Seminaire de probabilites et statistiques'', Universite Claude Bernard Lyon 1, Lyon, France.

RW kernels, spanning forests and multiscale analysis on graphs, 28 February 2017, “Colloquium mathematics'', Groningen, The Netherlands.

Random walks driven by interacting particle systems: recent results & some questions for the next future, 13 January 2017, workshop “New results and challenges with random walks in dynamic random environment'', Bristol, UK.

-2016

Random walks in cooling random environments, 13 December 2016, workshop “A guided tour through random media : on the occasion of the 60th birthday of Frank den Hollander.'' EURANDOM, Eindhoven, The Netherlands.

Multiresolution of functions on graphs: a probabilistic approach, 7 December 2016, “Stochastics seminar'', Utrecht, The Netherlands.

Groups, individuals and explorations in a network: some probabilistic tools, 25 November 2016, “Leiden Complex Networks Network (LCN2)" meeting, Faculty of Science, Leiden, The Netherlands.

Multiresolution of functions on graphs: a probabilistic approach, 16 November 2016, workshop “Large Scale Stochastic Dynamics'', Oberwolfach, Germany.

Random walks on Markovian environments with spectral gap and on some glassy systems, 16 September 2016, “Workshop on Stochastic Processes: in honour of Erwin Bolthausen's 70th birthday", Zurich, Switzerland.

Perturbation of Markov processes and applications to random environments, 14 March 2016, IME/USP, Sao Paulo, Brazil.

-2015

Random walks in Markovian environments: a perturbative approach, 14 October 2015, Stochastics Colloquium, TU-Eindhoven, The Netherlands.

Perturbations of Markov processes and applications in random environments, 23 July 2015, workshop “Stochastic Methods in Finance and Physics", Heraklion, Crete, Greece.

-2014

A random walk driven by an exclusion process: hydrodynamic limits and path large deviations, 11 December 2014, TU Delft, The Netherlands.

On some random forests with determinantal roots, 30 October 2014, “Oberseminar Stochastics". University of Bonn, Germany.

On some random forests with determinantal roots, 10 October 2014, “Mark Kac Seminar", Utrecht, The Netherlands.

On some random forests with determinantal roots, 15 September 2014, Workshop of the Leverhulme International Network Grant “Laplacians, Random Walks, Bose Gas, Quantum Spin Systems''. University of Bristol, UK.

On some random forests with determinantal roots, 9 August 2014, XVIII EBP (Escola Brasileira de Probabilidade), Mambucaba, Brazil.

On some random forests with determinantal roots, 1 August 2014, 37th SPA (Stochastic Process and their Applications) conference, invited session organised by Claudio Landim, Buenos Aires, Argentina.

On some random forests with determinantal roots, 3 July 2014, “Geanpyl: colloque de cloture". University of Nantes, France.

Local CLT for some convolution equations and for weakly self-avoiding walks, 22 January 2014, “Material Modeling Seminar", Weierstrass Institute (WIAS), Berlin, Germany.

-2013

Local CLT for some convolution equations and for weakly self-avoiding walks, 17 December 2013, La Sapienza, University of Rome, Italy.

Recent progresses in random walks in dynamical random environments, 17 September 2013, Workshop “Random Media'', TU Berlin, Germany.

Recent progresses in random walks in dynamical random environments, 13 September 2013, University of Marseille, France.

Symmetric exclusion as a random environment: hydrodynamic limits and large deviations, 8 July 2013, Oberseminar: ``Stochastic processes in physics and biology'', TU Berlin, Germany.

Symmetric exclusion as a random environment: hydrodynamic limits, 14 February 2013, Workshop “Dynamical and disordered systems'', CIRM, Marseille, France.

Random walks in fast and slowly mixing dynamical random environments, 10 January 2013, IMPA, Rio de Janeiro, Brazil.

-2012

Symmetric exclusion as a random environment: hydrodynamic limits, 13 December 2012, Mini-symposium “New perspectives in particle systems'', TU Delft, The Netherlands.

Random walks in dynamical random environments, 3 December 2012, La Sapienza, University of Rome, Italy.

Random walks in fast and slowly mixing dynamical random environments, 8 March 2012, University of Paris, Diderot-Paris 7, France.

A local central limit theorem for convolution equations and weakly self-avoiding walks, 24 February 2012, University of Marseille, France.

A local central limit theorem for weakly self-avoiding walks in continuous space, 17 February 2012, Workshop “The expanding art of expansions'', EURANDOM, Eindhoven, The Netherlands.

-2010

Law of large numbers and large deviations for a class of random walks in dynamic random environments, 11 January 2010, ROMATRE, University of Rome, Italy.

-2009

Random walks in dynamic random environments: LLN and LDP, 16 December 2009, Workshop “Dynamic random environments'', EURANDOM, Eindhoven, The Netherlands.

Large deviations for a random walk in a dynamic random environment, 30 June 2009, Summer School in Probability, PIMS-UBC, Vancouver, Canada.

8 Committees

Commissione Didattica, University of Florence: Member of the Teaching Committee at the mathematics department, DIMAI, Firenze, December 2023-present.

Networks Educational Committee, NWO, The Netherlands: Chairman (September 2018-August 2022) and member (June 2014-August 2018) of the Networks Educational Committee within the Dutch NWO Gravitation Program NETWORKS.

Library Committee, MI-Leiden: Member of the Library Committee at the mathematics department, MI, Leiden, September 2019- August 2023.

PhD opposition and hiring/selection committees: Committee member for ``Incarichi docenza II semestre 2023-2024, Scuola Ingegneria", at University of Florence, online presence, Florence, Italy, 2024; Committee member for an RTT vacancy (01/A3- MAT/06) at University of Florence, online presence, Florence, Italy, 2023; Committee member for an RTD-B vacancy (01/A3- MAT/06) at University of Florence, online presence, Florence, Italy, 2022; PhD defense of Elizaveta Arzhakova, thesis title: ``Scaling Limits in Algebra, Geometry, and Probability'', Leiden, The Netherlands, February 23, 2022; PhD defense of Weberson da Silva Arcanjo, thesis title: ``Random walk on the zero range process”, online presence, Belo Horizonte, Brazil, March 11, 2022 ; PhD defense of Valentina Apollonio, thesis title: ``Shaking the square box: a PCA approach to the Ising model”, online presence, Rome, Italy, June 23, 2021; Member of the PhD and Postdoc selection committees within the NWO Zwaartekracht project NETWORKS for the COFUND grant (the Marie Sklodowska-Curie Actions, funded by the European Commission) Period: Spring 2021; PhD defense of Matteo Sfragara, thesis title: ``Wireless Random-Access Networks and Spectra of Random Graphs”, Leiden, The Netherlands, October 27, 2020; Member of the PhD selection committee within the NWO Zwaartekracht project NETWORKS for the COFUND grant (the Marie Sklodowska-Curie Actions, funded by the European Commission).Period: June 2020; PhD defense of Matteo Quattropani, thesis title: ``Mixing and cover time on sparse random digraphs”, online presence, Rome, Italy, April 27, 2020; PhD defense of Janusz Meylahn, thesis title: ``Stochastic resetting and hierarchical synchronization'', Leiden, The Netherlands, September 24, 2019; PhD defense of Hakan Guldas, thesis title: ``Exploration on and of Networks", Leiden, The Netherlands, July 3, 2019; PhD defense of Andrea Roccaverde, thesis title: ``Breaking of ensemble equivalence for complex networks'', Leiden, The Netherlands, December 5, 2018; PhD defense of Andreas Stein Bethuelsen, thesis title: ``Random walks and the contact process'', Leiden, The Netherlands, November 22, 2016; PhD defense of Willem van Zuijlen, thesis title:``Gibbs-non-Gibbs transitions and vector-valued integration'', Leiden, The Netherlands, September 07, 2016; PhD defense of Herman Blok, thesis title: ``Unbounded-rate Markov decision processes: structural properties via a parametrisation approach'', Leiden, The Netherlands, June 23, 2016; PhD defense of Conrado Freitas Paulo da Costa, thesis title:``From reaction-diffusion models to the study of stochastic differential equations'', IMPA, Rio de Janeiro, Brazil, March 18, 2016; PhD defense of Renato Soares dos Santos, thesis title: ``Some case studies of random walks in dynamic random environments'', Leiden, The Netherlands, December 19, 2012

Master exams committees: DIMAI, Florence, for the following master students: Pietro Lotti (October 18, 2023); MI, Leiden, for the following master students: Sam Melief (October 6, 2021), Eduard Bosch (June 8, 2021), Josefien Verschuure (September 11, 2018), Lianne van der Velde (July 5, 2017), Vaya Sapobi Samui Vos (December 20, 2016), Giulia Pederzani (May 12, 2016), Dylan Gonzalez Arroyo (January 22, 2016).

9 Languages

Italian (mother tongue)

Dutch

English

Portuguese

Spanish

Luca AVENA

Interessi

AREAS: Probability theory, statistical physics and complex networks.

TOPICS: Markov chains, random walks, self-avoiding walks, branching random walks, random media, disordered systems, interacting particle systems, hydrodynamic limits, large deviations, metastability, spectral geometry, random graph ensembles, random partitioning, random spanning trees and forests, FK-percolation, networks renormalization, randomized algorithms for network analysis.

BRIEF DESCRIPTION: My scientific production is constituted by two main lines of investigation I am developing along the years: the first line is fundamental and concerns the study of the long term behaviour of key models of random processes in random environments in different geometrical settings (integer lattices, non-regular graphs and random graphs, possibly changing over time), the second line is more applied and aims at designing randomized algorithms to analyze network based data sets by using random walk kernels and random rooted forests.

Luca AVENA

Pubblicazioni

Legenda

Contributo su rivista |
Articolo su libro |
Libro |
Contributo in atti di convegno (proceeding) |
Brevetto |
Curatela |
Altro |
Tesi di Dottorato

Avena, Luca; da Costa, Conrado (2023). Laws of Large Numbers for Weighted Sums of Independent Random Variables: A Game of Mass. JOURNAL OF THEORETICAL PROBABILITY, pp. 0-0, ISSN:0894-9840 DOI

Avena L; Guldas H; van der Hofstad R; den Hollander F; Nagy O (2022). Linking the mixing times of random walks on static and dynamic random graphs. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 153, pp. 145-182, ISSN:0304-4149 DOI

Avena L; Gaudilliere A; Milanesi P; Quattropani M (2022). Loop-erased partitioning of a
graph: mean-field analysis. ELECTRONIC JOURNAL OF PROBABILITY, vol. 27, pp. 1-35, ISSN:1083-6489 DOI

Avena L; Chino Y; da Costa C; den Hollander F (2022). Random walk in cooling random environment: recurrence versus transience and mixed fluctuations. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, vol. 58, pp. 967-1009, ISSN:0246-0203 DOI Accesso ONLINE all'editore

Avena L; Castell F; Gaudillière A; Mélot C (2021). Approximate and Exact Solutions of Intertwining Equations Through Random Spanning Forests. In: Maria Eulália Vares, Roberto Fernández, Luiz Renato Fontes, Charles M. Newman. In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius., pp. 27-69 Springer, Birkhäuser, Cham. DOI

Avena L; Gün O; Hesse M (2020). The parabolic Anderson model on the hypercube. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 130, pp. 3369-3393, ISSN:0304-4149 DOI

Avena L; Castell F; Gaudillière A; Mélot C (2020). Intertwining wavelets or multiresolution analysis on graphs through random forests. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, vol. 48, pp. 949-992, ISSN:1063-5203 DOI

Avena L; Chino Y; da Costa C; den Hollander F (2019). Random walk in cooling random environment: ergodic limits and concentration inequalities. ELECTRONIC JOURNAL OF PROBABILITY, vol. 24, pp. 1-35, ISSN:1083-6489 DOI

Avena L; den Hollander F (2019). Random Walks in Cooling Random Environments. . Sojourns in Probability Theory and Statistical Physics - III, pp. 23-42, Singapore: Springer, Singapore. DOI

Barthelme S; Tremblay N; Gaudilliere A; Avena L; Amblard P-O (2019). Estimating the inverse trace using random forests on
graphs. In: GRETSI 2019 - XXVIIème Colloque francophone de traitement du signal et des images, Lille, France., August 2019. Accesso ONLINE all'editore

Avena L; Güldaş H: van der Hofstad R: den Hollander F (2019). Random walks on dynamic configuration models:A trichotomy. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 129, pp. 3360-3375, ISSN:0304-4149 DOI

Avena L; Gaudillière A (2018). Two Applications of Random Spanning Forests. JOURNAL OF THEORETICAL PROBABILITY, vol. 31, pp. 1975-2004, ISSN:0894-9840 DOI

Avena L; Jara M; Völlering F (2018). Explicit LDP for a slowed RW driven by a symmetric exclusion process. PROBABILITY THEORY AND RELATED FIELDS, vol. 171, pp. 865-915, ISSN:0178-8051 DOI

Avena L; Blondel O; Faggionato A (2018). Analysis of random walks in dynamic random environments via L2-perturbations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 128, pp. 3490-3530, ISSN:0304-4149 DOI

Avena L; Castell F; Gaudillière A; Mélot C (2018). Random Forests and Networks Analysis. JOURNAL OF STATISTICAL PHYSICS, vol. 173, pp. 985-1027, ISSN:0022-4715 DOI

Avena L; Gaudillière A (2018). A proof of the transfer-current theorem in absence of reversibility. STATISTICS & PROBABILITY LETTERS, vol. 142, pp. 17-22, ISSN:0167-7152 DOI

Avena L; Güldaş H; van der Hofstad R; den Hollander F (2018). Mixing times of random walks on dynamic configuration models. THE ANNALS OF APPLIED PROBABILITY, vol. 28, pp. 1977-2002, ISSN:1050-5164 DOI

Avena L; Bolthausen E; Ritzmann C (2016). A local CLT for convolution equations with an application to weakly self-avoiding random walks. ANNALS OF PROBABILITY, vol. 44, pp. 206-234, ISSN:0091-1798 DOI

Avena L; Blondel O; Faggionato A (2016). A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model. JOURNAL OF STATISTICAL PHYSICS, vol. 165, pp. 1-23, ISSN:0022-4715 DOI

Avena L; Franco T; Jara M; Völlering F (2015). Symmetric exclusion as a random environment: Hydrodynamic limits. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, vol. 51, pp. 901-916, ISSN:0246-0203 DOI

Avena L; dos Santos R; Völlering F (2013). Transient random walk in symmetric exclusion: limit theorems and an Einstein relation. ALEA, vol. 10, pp. 693-709, ISSN:1980-0436 Accesso ONLINE all'editore

Avena L (2012). Symmetric exclusion as a model of non-elliptic dynamical random conductances. ELECTRONIC COMMUNICATIONS IN PROBABILITY, vol. 17, pp. 1-8, ISSN:1083-589X DOI

Avena L; Thomann P (2012). Continuity and Anomalous Fluctuations in Random Walks in Dynamic Random Environments: Numerics, Phase Diagrams and Conjectures. JOURNAL OF STATISTICAL PHYSICS, vol. 147, pp. 1041-1067, ISSN:0022-4715 DOI

Avena L; den Hollander F; Redig F (2011). Law of large numbers for a class of random walks in dynamic random environments. ELECTRONIC JOURNAL OF PROBABILITY, vol. 16, pp. 587-617, ISSN:1083-6489 DOI

Avena L; den Hollander F; Redig F (2010). Large deviation principle for one-dimensional random walk in dynamic random environment: attractive spin-flips and simple symmetric exclusion. MARKOV PROCESSES AND RELATED FIELDS, vol. 16, pp. 139-168, ISSN:1024-2953

Luca AVENA

Curriculum

1. Academic positions

Date: 01/09/2023-present Position: Associate Professor, Institution: University of Florence, DIMAI, Italy.

Date: from 01/03/2021-31/08/2023, Position: Associate Professor (UHD), Institution: University of Leiden, MI, The Netherlands.

Date: 15/10/2019-14/10/2021 & 15/11/2023-14/11/2025, Position: Visiting Professorship in “Mathematical theory of Complex Networks”, Institution: IMT School for Advanced Studies Lucca, Lucca, Italy.

Date: 01/06/2020-28/02/2021 Position: Assistant Professor (UD), Institution: University of Leiden, MI, The Netherlands.

Date: 01/06/2014-31/05/2020, Position: Assistant Professor (Tenure Track), funded by the NWO Gravitation Program NETWORKS, Institution: University of Leiden, MI, The Netherlands.

Date: 01/04/2013-31/05/2014, Position: Post-doc in the group of Prof. Dr. Wolfgang König, Institution: Weierstrass Institute (WIAS), Berlin, Germany.

Date: 01/11/2010-31/03/2013, Position: Post-doc in the group of Prof. Dr. Erwin Bolthausen, Institution: Department of Mathematics, University of Zürich, Switzerland.

2. Academic education

PhD in Mathematics Institution:Leiden University, Period:2006-2010, Date of PhD award:26/10/2010, Supervisor:Prof. Dr. Frank den Hollander, Thesis title: Random Walks in Dynamic Random Environments.

Master’s degree in Mathematics (cum laude) Institution:Università di Roma ROMATRE, Date:July2006, Supervisor:Prof. Dr. Fabio Martinelli, Thesis title: On the threshold of the random k-sat.

Bachelor’s degree in Mathematics Institution:Università di Roma ROMATRE, Date:July2004.

Erasmus student Institution:Universidad de Granada, Spain, Date:2002-2003.

3. Academic Teaching

ASN Italian habilitation Abilitazione Scientifica Nazionale, both as Full Professor (I fascia) and as Associate Professor (II fascia) for 01/A3 Analisi Matematica, Probabilità e Statistica Matematica. Obtained on February 6,2023, from MIUR (Ministero dell’ Istruzione e del Merito), Italy,https://abilitazione.miur.it/public/pubblicarisultati_2021.php.

BKO Dutch habilitation Basis Kwalificatie Onderwijs, Leiden, The Netherlands. Obtained on October24,2017.

Instructor, Florence University:

Course title:Calcolo delle Probabilità. Period: Fall2023. Given jointly with G. Bet. Course for bachelor students in mathematics.

Course title:Analisi Matematica II & Probabilità. Period: Fall2023. Given jointly with G. Giovannardi and I. Lucardesi. Course for master students in engineering (ingegneria informatica).

Instructor, Leiden University:

Course title: Complex Networks. Period: Fall 2022. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Markov chains and applications. Period: Fall 2022. Course for master students in mathematics.

Course title: Stochastic Processes. Period: Spring 2022. Given jointly with F. den Hollander and G. Bonnet within the national program MASTERMATH.

Course title: Complex Networks. Period: Fall 2021. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Markov chains and applications. Period: Fall 2021. Course for master students in mathematics.

Course title: Interacting Particle Systems. Period: Fall 2020. Within the national program MASTERMATH.

Course title: Complex Networks. Period: Fall 2020. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Introduction to Probability Theory (Inleiding Kansrekening). Period: Spring 2020.

Course title: Complex Networks. Period: Fall 2019. Given jointly with M. Emmerich and D. Garlaschelli. Multidisciplinary course for master and bachelor students in astronomy, computer science, mathematics and physics.

Course title: Probability Seminar: Stories from Asymptopia. Period: Fall 2019. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Course title: Introduction to Probability Theory (Inleiding Kansrekening). Period: Spring 2019. Course for bachelor students in mathematics.

Course title: Stochastic Models for Genetic Evolution. Period: Spring 2019. Given jointly with F. den Hollander. Course for master students in mathematics.

Course title: Probability Seminar: Random Graph Ensembles. Period: Fall 2018. Given jointly with F. den Hollander. Course for master students in mathematics.

Course title: Introduction to Probability Theory (Inleiding Kansrekening). Period: Spring 2018. Course for bachelor students in mathematics.

Course title: Introduction to Stochastic Processes. Period: Spring 2018. Given jointly with F. Spieksma within the national program MASTERMATH.

Course title: Probability Seminar: Random Walks in Random Environments. Period: Fall 2017. Given jointly with F. den Hollander. Course for master students in mathematics.

Course title: Stochastic Models for Genetic Evolution. Period: Spring 2017. Course for master students in mathematics.

Course title: Probability Seminar: Large Deviations & Applications. Period: Fall 2016. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Course title: Random Walks, Period: Fall 2016. Course for bachelor and master students in mathematics.

Course title: Coupling Theory. Period: Spring 2016. Course for master students in mathematics.

Course title: Random Walks. Period: Fall 2015. Course for bachelor and master students in mathematics.

Course title: Probability Seminar: Random Matrix Theory. Period: Fall 2015. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Course title: Stochastic Models for Genetic Evolution. Period: Spring 2015. Course for master students in mathematics.

Course title: Probability Seminar: Large Deviations & Applications. Period: Fall 2014. Given jointly with E. Vierbitskiy. Course for master students in mathematics.

Teaching Assistant:

(Zürich University) Logic, Fall 2012, Instructor: L. Halbeisen (Department of Mathematics, Zürich University);

(Zürich University) Probability Theory, Spring 2012, Instructor: J. Najnudel ;

(Zürich University) Probability Theory, Spring 2011, Instructor: J. Najnudel ;

(Leiden University) Statistiek voor LST, Spring 2010, Instructor: R.J. Kooman ;

(Leiden University) Wiskunde 2 voor LST, Spring 2009, Instructor: R.J. Kooman;

(Leiden University) Maat en Integratietheorie, Fall 2008, Instructor: F. Redig;

(Leiden University) Applied Analysis, Fall 2007, Instructor: V. Rottschäfer.

(ROMATRE University) Probability Theory 1 (CP1), Spring 2006, Instructor: F. Martinelli;

(ROMATRE University) Probability Theory 1 (CP1), Spring 2005, Instructor: F. Martinelli.

4. Academic Supervisions

PostDoc:

Rangel Baldasso, MI, Leiden. Topic: Contact process and voter model on random graphs. Period: May 2020- May 2023.

Matteo Quattropani, MI, Leiden. Topic: Metastability for interacting particle systems on random graphs. Period: Sept. 2021-Aug. 2022.

Conrado da Costa, MI, Leiden. Topic: Random motion in random environments. Period: Sept. 2016-Sept.2019.

Yuki Chino, MI, Leiden. Topic: Random walks in cooling random environments. Co-supervisor: F. den Hollander. Period: Sept. 2017-Sept. 2019

PhD:

Nandan Malhotra, MI, Leiden. Topic: spectra of random graph ensembles. Co-supervisor: R. Hazra. Start: September 1, 2021.

Federico Capannoli, MI, Leiden. Topic: voter model on random graphs. Co-supervisor: R. Hazra. Start: September 1, 2021.

Margherita Lalli, PhD candidate at IMT, Lucca, under the supervison of D. Garlaschelli. One year internship in Leiden under my supervision within the Erasmus+ programme. Topic: Spectral properties of random graphs. Period: April 2021/August 2022.

Twan Koperberg, MI, Leiden. Topic: Random rooted forests and exploration of sparse networks. Co-supervisor: A. Gaudilliere. Start: March 1, 2020.

Oliver Nagy, MI, Leiden. Topic: Random walks on dynamic random graphs. Co-supervisors: F. den Hollander and R. van der Hofstad. Start: February 1, 2020.

Hakan Guldas, MI, Leiden. Thesis title: ``Random walks on dynamic random graphs”. Co-supervisors: F. den Hollander and R. van der Hofstad. Defended on July 3, 2019.

Master:

Niels Kolebrander, MI, Leiden. Thesis title: "Statistical properties for a class of random billiards''. Co-supervisor: D. Terhesiu (2023).

Irina Gurewitsch, MI, Leiden. Thesis title: ``Using random rooted spanning forest for network immunization''. Co-supervisor: M. Emmerich (2022).

Vittorio Magrini, MI, Leiden. Thesis title: ``Local limits of random rooted spanning trees and forests on dense geometries" Co-supervisor: C. da Costa (2020).

Bruno Stordeur, Universite d'Aix-Marseille, Marseille, one month internship in Leiden as part of his master project, topic: Wavelets for signals on graphs. Co-supervisors: Fa. Castell and C. Melot (June 2019).

Adi Kiang, MI, Leiden. Thesis title: ``Networks coarse-graining through intertwining dualities”. Co-supervisor: F. den Hollander (2019).

Khadija Lachhab, MI, Leidem. Thesis title: ``Wright-Fisher model with seed bank and selection”. Co-supervisor: F. den Hollander (2019).

Thomas van Hees, MI, Leiden. Thesis topic: Networks filtering through discrete curvatures. Co-supervisor: D. Garlaschelli (2018).

Alvin Peters, MI, Leiden. Thesis title: ``Electrical networks and Markov chains: Classical results and beyond”. Co-supervisor: S. Taati (2016).

Matteo Quattropani, MI, Leiden. Thesis title: ``Spectral techniques of Community Detection: a probabilistic perspective”. Co-supervisor: D. Garlaschelli (2016).

Bachelor:

Giovanni Pepe, DIMAI, Firenze. Topic ``Semicircle law and spectra of random graphs'', co-supervisor: G. Bet (2024).

Bob Vermulen, MI, Leiden. Thesis title: ``Local convergence of random graphs'', co-supervisor: R. Baldasso (2022).

Jochem Boelema, MI, Leiden. Thesis title: ``Introduction to renormalization techniques in percolation theory'', co-supervisor: R. Baldasso (2021).

Niels Kolebrander, MI, Leiden. Thesis title: ``Billiards, random walks and gases: some case studies'', co-supervisor: D. Terhesiu (2021).

Jannetje Driessen, MI, Leiden. Thesis title: ``Loop-Erased Partitions on Tree Structures" (2019).

Twan Koperberg, MI, Leiden. Thesis title: ``Couplings and Matching: On the equivalence of Strassen's theorem and some combinatorial theorems'', co-supervisor: S. Taati (2016)

5. Research Production

Pubblications:

L. Avena and C. da Costa, Laws of large numbers for weighted sums of independent random variables: a game of mass, Journal of Theoretical Probability, https://doi.org/10.1007/s10959-023-01296-z (2023).

L. Avena, H. Guldas, R. van der Hofstad, F. den Hollander and O. Nagy, Linking the mixing times of random walks on static and dynamic random graphs, Stochastic Processes and their Applications 153, 145-182 (2022).

L. Avena, A. Gaudilliere, P. Milanesi and M. Quattropani, Loop-erased partitioning of a graph: mean-field analysis, Electronic Journal of Probability 27 (67), 1-35 (2022).

L. Avena, Y. Chino, C. da Costa and F. den Hollander, Random walk in cooling random environment: recurrence versus transience and mixed fluctuations, Annals de l’Institut Henri Poincare, Probability and Statistics 58 (2), 967-1009 (2022).

L. Avena, F. Castell, A. Gaudilliere, and C. Melot, Approximate and exact solutions of intertwining equations through random spanning forests, In and Out of Equilibrium 3. Celebrating Vladas Sidoravicius, Progress in Probability 77, Springer (2021).

L. Avena, F. Castell, A. Gaudilliere and C. Melot, Intertwining wavelets or multiresolution analysis on graphs through random forests, Applied and Computational Harmonic Analysis 48 (3), 949-992 (2020).

L. Avena, O. Gun and M. Hesse, The parabolic Anderson model on the hypercube, Stochastic Processes and their Applications} 130 (6), 3369-3393 (2020).

L. Avena, H. Guldas, R. van der Hofstad and F. den Hollander, Random walks on dynamic configuration models: a trichotomy, Stochastic Processes and their Applications 129 (9), 3360-3375 (2019).

L. Avena and F. den Hollander, Random walks in cooling random environments, Sojourns in Probability Theory and Statistical Physics–III, A Festschrift for Charles M. Newman, Springer, Proceedings in Mathematics & Statistics series}, Vol. 300, 23-42 (2019).

S. Barthelme, N. Tremblay, A. Gaudilliere, L. Avena and P.-O. Amblard, Estimating the inverse trace using random forests on graphs, Proceedings GRETSI Symposium on Signal and Image Processing, Lille, France (2019). Available on ArXiv:1905.02086 (2019).

L. Avena, Y. Chino, C. da Costa and F. den Hollander, Random walk in cooling random environment: ergodic limit and concentration inequalities, Electronic Journal of Probability 24(38), 1-35 (2019).

L. Avena, F. Castell, A. Gaudilliere and C. Melot, Random forests and networks analysis, Journal of Statistical Physics 173(3-4), 985-1027 (2018).

L. Avena, H. Guldas, R. van der Hofstad and F. den Hollander, Mixing times of random walks on dynamic configuration models, Annals of Applied Probability 28(4), 1977-2002 (2018).

L. Avena and A. Gaudilliere, A proof of the transfer-current theorem in absence of reversibility, Statistics and Probability Letters 142, 17-22 (2018).

L. Avena, M. Jara and F. Vollering, Explicit LDP for a slowed RW driven by a symmetric exclusion process, Probability Theory and Related Fields 171(3-4), 865-915 (2018).

L. Avena, O. Blondel and A. Faggionato, Analysis of random walks in dynamic random environments via L2- perturbations, Stochastic Processes and their Applications 128(10), 3490-3530 (2018).

L. Avena and A. Gaudilliere, Two applications of random spanning forests, Journal of Theoretical Probability 31(4), 1975-2004 (2018).

L. Avena, O. Blondel and A. Faggionato, A class of random walks in reversible dynamic environments: antisymmetry and applications to the east model, Journal of Statistical Physics 165, 1-23 (2016).

L. Avena, E. Bolthausen and C. Ritzmann, A local CLT for convolution equations with an application to weakly self-avoiding random walks, Annals of Probability 44 (1), 206-234 (2016).

L. Avena, T. Franco, M. Jara and F. Vollering, Symmetric exclusion as a random environment: hydrodynamic limits, Annals de l’Institut Henri Poincare, Probability and Statistics 51 (3), 901-916 (2015).

L. Avena, R. dos Santos and F. Vollering, Transient random walk in symmetric exclusion: limit theorems and an Einstein relation, ALEA, Latin American Journal of Probability and Mathematical Statistics 10 (2), 693-709 (2013).

L. Avena, Symmetric exclusion as a model of non-elliptic dynamical random conductances, Electronic Communications in Probability 17 (44), 1-8 (2012).

L. Avena and P. Thomann, Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures, Journal of Statistical Physics 147, 1041-1067 (2012).

L. Avena, F. den Hollander and F. Redig, Law of large numbers for a class of random walks in dynamic random environments, Electronic Journal of Probability 16, 587-617 (2011).

L. Avena, F. den Hollander and F. Redig, Large deviation principle for one-dimensional random walk in dynamic random environment: attractive spin-flips and simple symmetric exclusion, Markov Processes and Related Fields 16, 139-168 (2010).

L. Avena, Random Walks in Dynamic Random Environments, Ph.D. thesis. Available on the online catalogue of the Leiden University Library: www.catalogus.leidenuniv.nl, Leiden (2010).

Preprints:

L. Avena, F. Capannoli, R. S. Hazra, M. Quattropani, Meeting, coalescence and consensus time on random directed graphs, ArXiv:2308.01832 (2023). To appear in Annals of Applied Probability.

L. Avena, D. Garlaschelli, R. S. Hazra, M. Lalli, Inhomogeneous random graphs with infinite-mean fitness variables, ArXiv:2212.08462 (2022). To appear in Journal of Applied Probability.

L. Avena, R. Baldasso, R. S. Hazra, F. den Hollander, M. Quattropani, Discordant edges for the voter model on regular random graphs, ArXiv:2209.01037 (2022). To appear in ALEA, Latin American Journal of Probability and Mathematical Statistics.

L. Avena, C. da Costa and J. Peterson, Gaussian, stable, tempered stable and mixed limit laws for random walks in cooling random environments, ArXiv:2108.08396 (2021). To appear in Annals de l’Institut Henri Poincare, Probability and Statistics

L. Avena, J. Driessen and T. Koperberg, Loop-erased partitioning of a network: monotonicities & analysis of cycle-free graphs, ArXiv:2103.14436 (2021).

L. Avena, C. da Costa and F. den Hollander, Stochastic models for genetic evolution, Lecture notes, Mathematisch Instituut, Universiteit Leiden. Available at https://websites.math.leidenuniv.nl/probability/lecturenotes/BioStoch.pdf (2019).

L. Avena, M. Heydenreich, F. den Hollander, E. Verbitskiy and W. van Zuijlen, Random walks, Lecture notes, Mathematisch Instituut, Universiteit Leiden. Available at https://websites.math.leidenuniv.nl/probability/lecturenotes/RandomWalks.pdf (2016).

L. Avena and A. Gaudilliere, Random spanning forests, Markov matrix spectra and well distributed points, ArXiv:1310.1723 (2013).

6 Events Organisation

Workshop ``The Lorentz Gas'', December 19-23, 2022, Lorentz Center, Leiden, The Netherlands.

Workshop ``Celebrating Francesca Romana Nardi: a life in probability, building communities across Europe'', July 18-22, 2022, Aula Magna, Florence, Italy.

13-th NETWORKS TRAINING WEEK, May 9-12, 2022, De Schildkamp, Asperen,The Netherlands. See https://www.thenetworkcenter.nl/Education/Training-Weeks/

ICM 2018 satellite conference ``Topics in Mathematical Physics'', session on ``Complex Networks'', July 26-31, 2018. Sao Paulo, Brazil.

Workshop ``Random structures on the brain'', December 4-8, 2017, Lorentz Center, Leiden, The Netherlands.

Workshop ``Community Detection & Networks Reconstruction'', September 19-22, 2017, EURANDOM, Eindhoven, The Netherlands.

Workshop ``Randomness and Graphs: Processes and Structures'', September 11-15, 2017, EURANDOM, Eindhoven, The Netherlands.

XVI YEP (Young European Probabilists) workshop ``Networks: Probability, Combinatorics and Algorithms'', September 04-08, 2017, EURANDOM, Eindhoven, The Netherlands.

Stochastic Activity Month ``Random Graphs and Complex Networks: models, algorithms and applications'', September 2017, EURANDOM, Eindhoven, The Netherlands.

Workshop ``New results and challenges with random walks in dynamic random environment'', 11-13 January, 2017, Bristol, UK.

XIII YEP (Young European Probabilists) workshop ``Large Deviations for Interacting Particle Systems and Partial Differential Equations'', March 7-11, 2016, EURANDOM, Eindhoven, The Netherlands.

Stochastic Activity Month ``Probability and Analysis'', March 2016, EURANDOM, Eindhoven, The Netherlands.

Workshop ``Random Motion in Random Media'', 30 March-2 April, 2015, EURANDOM, Eindhoven, The Netherlands.

Stochastic Activity Month ``Random Walk and Random Media'', 23 March-24 April, 2015, EURANDOM, Eindhoven, The Netherlands.

16th Rencontres Mathematiques de Rouen, June 18-20, 2014, Rouen, France.

7 Selected Invited Talks

-2023

Meetings of random walks & consensus dynamics on random directed graphs, 30 January 2024, ICTS-NETWORKS WORKSHOP “CHALLENGES IN NETWORKS”, ICTS, Bangalore, India.

Meetings of random walks & consensus dynamics on sparse random digraphs, 23 November 2023, IMT Lucca, Italy.

Walking with Frank in various changing landscapes, 29 September 2023, workshop“New frontiers in Probability", Leiden, The Netherlands.

Tempi di mescolamento per camminate aleatorie su reti dinamiche, 8 September 2023, XXII Congresso dell'Unione Matematica Italiana, UMI, invited session organised by Elisabetta Candellero and Dario Trevisan, Pisa, Italy.

Meetings of random walks and consensus in voter dynamics on sparse random digraphs, workshop“Random walks in Bath", 7 June 2023, Wolfson Amphitheater, Bath, UK.

A network randomized k-centrality measure & applications to node immunization, 24 February 2023,“Leiden Complex Networks Network (LCN2)" meeting, Faculty of Science, Leiden, The Netherlands.

Evolution of discordances in voter dynamics on random regular graphs, online, 12 January 2023, workshop“Probabilistic Methods in Statistical Mechanics of Random Media and Random Fields 2023", Fukuoka, Japan.

-2022

A randomized k-centrality measure & applications to networks node immunization, 6 December 2022, Eindhoven SPOR Seminar, Eurandom, Eindhoven, The Netherlands.

Anomalous fluctuations for random walks in dynamic random environments with resetting, 30 June 2022, IMS Annual Meeting in Probability and Statistics, invited session organised by Jonathon Peterson, London, UK.

Evolution of discordances in voter dynamics on random regular graphs, 15 June 2022, “Third italian meeting on Probability and Mathematical Statistics", Bologna, Italy.

A randomized k-centrality measure & applications to networks node immunization, 7 June 2022, General Mathematics Colloquium, UvA, Amsterdam, The Netherlands.

A randomized k-centrality measure & applications to networks node immunization, 30 May 2022, workshop “A day on Random Graphs”, TOR VERGATA, University of Rome, Italy.

-2021

Node immunization in networks: a scalable searching algorithm based on random rooted forests, online, 1 June 2021, IMT Lucca, Italy.

Random walks in cooling random environments: a journey on the one-dimensional lattice, online, 17 May 2021. Mathematics Department, Universidad Federal de Rio de Janeiro, Brazil.

Explorations of networks through random rooted forests, online, 6 April 2021, NMC, Nederlands Mathematisch Congres, 2021, The Netherlands.

Node immunization in networks: a scalable searching algorithm based on random rooted forests, online, 26 February 2021, Mathematics Department, Universita' degli studi di Padova, Italy.

-2020

Node immunization in networks: a scalable searching algorithm based on random rooted forests, online, 14 October 2020, Mathematics Department, Universidad Federal de Bahia, Salvador, Brazil.

Mixing time for RW on dynamic configuration model, 15 January 2020, workshop “Spectra, Algorithms and Random Walks on Random Networks”, CIRM Marseille, France.

-2019

Mesoscopic explorations of graphs through random rooted forests, 27 November 2019, workshop “Brain networks and metastability”, IMT Lucca, Italy.

Renormalisation for graphs and signals on graphs via random walk kernels, 25 November 2019, workshop “Network coarse-graining”, IMT Lucca, Italy.

Explorations of networks through random spanning forests: theory and applications, 22 November 2019, AN “AUTUMN” DAY IN PROBABILITY AND STATISTICAL PHYSICS, Florence, Italy.

Multiscale analysis of network data sets via random walk kernels, 20 November 2019, University of Pisa, Italy.

Processing data sets on networks: rooted forests and other probabilistic tools, 16 July 2019, conference “Complex networks: from socio-economic systems to biology and brain'' , Lipari, Sicily, Italy.

Processing data sets on networks: random forests and other probabilistic tools, 18 June 2019, “Second italian meeting on Probability and Mathematical Statistics", Vietri sul Mare (Salerno), Italy.

Sinai walk in cooling random environment, 30 May 2019, ``Japanese-Dutch meeting", Lorentz Center, Leiden, The Netherlands.

Random walks in cooling random environments, 21 May 2019, Max Planck Institute, Leipzig, Germany.

Network data-sets: randomized decomposition through forests and some related tools, 15 April 2019, Lecture day on the occasion of Ravi Kumar's visit, TU Eindhoven, The Netherlands.

Mixing time on dynamic configuration model, 15 January 2019, mathematics and physics department, Roma tre University, Rome, Italy.

-2018

Loop-erased partitioning: two-point correlations on mean-field models, 12 December 2018, Groningen Stochastics Seminar, Groningen, The Netherlands.

Network coarse-graining, Markov intertwining and metastability without asymptotics, 27 July 2018, conference “Topics in Mathematical Physics", ICM 2018 satellite conference, Sao Paul, Brazil.

Data sets on networks: some probabilistic tools and a new wavelet transform, 24 July 2018, Facultad de Ingeniera, Buenos Aires, Argentina.

Network coarse-graining, Markov intertwining and metastability without asymptotics, 17 July 2018, workshop ``Geometry and scaling of random structures", CIMPA School and X Escuela Santala, ICM 2018 satellite workshop, Buenos Aires, Argentina.

Random walks in cooling random environments, 11 June 2018, 40th SPA (Stochastic Process and their Applications) conference, invited session organised by Marton Balasz, Gothenburg, Sweden.

Network coarse-graining, Markov intertwining and a framework for metastability without asymptotics, 9 June 2018, workshop “ISI-NETWORKS Day'', Lipsius building, Leiden, The Netherlands.

Random walks in cooling random environments, 30 May 2018, FRANCO-DUTCH YEP-workshop “Mathematical statistical mechanics, random graphs and related topics'' EURANDOM, Eindhoven, The Netherlands .

Some probabilistic tools to process data sets on networks, 9 May 2018, workshop ``Brainstorm Day, Complex Networks'', Lorentz Center, Leiden, The Netherlands.

-2017

Data sets on networks: some probabilistic tools, 13 December 2017, workshop “Network Models: Structure and Function'', Oberwolfach, Germany.% 11-16 December 2017.

Data sets on networks: some probabilistic tools, 28 November 2017, series of lectures “This week's discoveries", Faculty of Science, Leiden, The Netherlands.

Minicourse: Random walks, forests and network analysis, 30 October-3 November 2017, 5th NETWORKS TRAINING WEEK, De Schildkamp, Asperen, The Netherlands.

A taste of randomness and disorder for lunch, 5 April 2017, lunch lecture for De Leidsche Flesch student association, Leiden, The Netherlands.

RW kernels, spanning forests and multiscale analysis on graphs, 1 March 2017, “Seminaire de probabilites et statistiques'', Universite Claude Bernard Lyon 1, Lyon, France.

RW kernels, spanning forests and multiscale analysis on graphs, 28 February 2017, “Colloquium mathematics'', Groningen, The Netherlands.

Random walks driven by interacting particle systems: recent results & some questions for the next future, 13 January 2017, workshop “New results and challenges with random walks in dynamic random environment'', Bristol, UK.

-2016

Random walks in cooling random environments, 13 December 2016, workshop “A guided tour through random media : on the occasion of the 60th birthday of Frank den Hollander.'' EURANDOM, Eindhoven, The Netherlands.

Multiresolution of functions on graphs: a probabilistic approach, 7 December 2016, “Stochastics seminar'', Utrecht, The Netherlands.

Groups, individuals and explorations in a network: some probabilistic tools, 25 November 2016, “Leiden Complex Networks Network (LCN2)" meeting, Faculty of Science, Leiden, The Netherlands.

Multiresolution of functions on graphs: a probabilistic approach, 16 November 2016, workshop “Large Scale Stochastic Dynamics'', Oberwolfach, Germany.

Random walks on Markovian environments with spectral gap and on some glassy systems, 16 September 2016, “Workshop on Stochastic Processes: in honour of Erwin Bolthausen's 70th birthday", Zurich, Switzerland.

Perturbation of Markov processes and applications to random environments, 14 March 2016, IME/USP, Sao Paulo, Brazil.

-2015

Random walks in Markovian environments: a perturbative approach, 14 October 2015, Stochastics Colloquium, TU-Eindhoven, The Netherlands.

Perturbations of Markov processes and applications in random environments, 23 July 2015, workshop “Stochastic Methods in Finance and Physics", Heraklion, Crete, Greece.

-2014

A random walk driven by an exclusion process: hydrodynamic limits and path large deviations, 11 December 2014, TU Delft, The Netherlands.

On some random forests with determinantal roots, 30 October 2014, “Oberseminar Stochastics". University of Bonn, Germany.

On some random forests with determinantal roots, 10 October 2014, “Mark Kac Seminar", Utrecht, The Netherlands.

On some random forests with determinantal roots, 15 September 2014, Workshop of the Leverhulme International Network Grant “Laplacians, Random Walks, Bose Gas, Quantum Spin Systems''. University of Bristol, UK.

On some random forests with determinantal roots, 9 August 2014, XVIII EBP (Escola Brasileira de Probabilidade), Mambucaba, Brazil.

On some random forests with determinantal roots, 1 August 2014, 37th SPA (Stochastic Process and their Applications) conference, invited session organised by Claudio Landim, Buenos Aires, Argentina.

On some random forests with determinantal roots, 3 July 2014, “Geanpyl: colloque de cloture". University of Nantes, France.

Local CLT for some convolution equations and for weakly self-avoiding walks, 22 January 2014, “Material Modeling Seminar", Weierstrass Institute (WIAS), Berlin, Germany.

-2013

Local CLT for some convolution equations and for weakly self-avoiding walks, 17 December 2013, La Sapienza, University of Rome, Italy.

Recent progresses in random walks in dynamical random environments, 17 September 2013, Workshop “Random Media'', TU Berlin, Germany.

Recent progresses in random walks in dynamical random environments, 13 September 2013, University of Marseille, France.

Symmetric exclusion as a random environment: hydrodynamic limits and large deviations, 8 July 2013, Oberseminar: ``Stochastic processes in physics and biology'', TU Berlin, Germany.

Symmetric exclusion as a random environment: hydrodynamic limits, 14 February 2013, Workshop “Dynamical and disordered systems'', CIRM, Marseille, France.

Random walks in fast and slowly mixing dynamical random environments, 10 January 2013, IMPA, Rio de Janeiro, Brazil.

-2012

Symmetric exclusion as a random environment: hydrodynamic limits, 13 December 2012, Mini-symposium “New perspectives in particle systems'', TU Delft, The Netherlands.

Random walks in dynamical random environments, 3 December 2012, La Sapienza, University of Rome, Italy.

Random walks in fast and slowly mixing dynamical random environments, 8 March 2012, University of Paris, Diderot-Paris 7, France.

A local central limit theorem for convolution equations and weakly self-avoiding walks, 24 February 2012, University of Marseille, France.

A local central limit theorem for weakly self-avoiding walks in continuous space, 17 February 2012, Workshop “The expanding art of expansions'', EURANDOM, Eindhoven, The Netherlands.

-2010

Law of large numbers and large deviations for a class of random walks in dynamic random environments, 11 January 2010, ROMATRE, University of Rome, Italy.

-2009

Random walks in dynamic random environments: LLN and LDP, 16 December 2009, Workshop “Dynamic random environments'', EURANDOM, Eindhoven, The Netherlands.

Large deviations for a random walk in a dynamic random environment, 30 June 2009, Summer School in Probability, PIMS-UBC, Vancouver, Canada.

8 Committees

Commissione Didattica, University of Florence: Member of the Teaching Committee at the mathematics department, DIMAI, Firenze, December 2023-present.

Networks Educational Committee, NWO, The Netherlands: Chairman (September 2018-August 2022) and member (June 2014-August 2018) of the Networks Educational Committee within the Dutch NWO Gravitation Program NETWORKS.

Library Committee, MI-Leiden: Member of the Library Committee at the mathematics department, MI, Leiden, September 2019- August 2023.

PhD opposition and hiring/selection committees: Committee member for ``Incarichi docenza II semestre 2023-2024, Scuola Ingegneria", at University of Florence, online presence, Florence, Italy, 2024; Committee member for an RTT vacancy (01/A3- MAT/06) at University of Florence, online presence, Florence, Italy, 2023; Committee member for an RTD-B vacancy (01/A3- MAT/06) at University of Florence, online presence, Florence, Italy, 2022; PhD defense of Elizaveta Arzhakova, thesis title: ``Scaling Limits in Algebra, Geometry, and Probability'', Leiden, The Netherlands, February 23, 2022; PhD defense of Weberson da Silva Arcanjo, thesis title: ``Random walk on the zero range process”, online presence, Belo Horizonte, Brazil, March 11, 2022 ; PhD defense of Valentina Apollonio, thesis title: ``Shaking the square box: a PCA approach to the Ising model”, online presence, Rome, Italy, June 23, 2021; Member of the PhD and Postdoc selection committees within the NWO Zwaartekracht project NETWORKS for the COFUND grant (the Marie Sklodowska-Curie Actions, funded by the European Commission) Period: Spring 2021; PhD defense of Matteo Sfragara, thesis title: ``Wireless Random-Access Networks and Spectra of Random Graphs”, Leiden, The Netherlands, October 27, 2020; Member of the PhD selection committee within the NWO Zwaartekracht project NETWORKS for the COFUND grant (the Marie Sklodowska-Curie Actions, funded by the European Commission).Period: June 2020; PhD defense of Matteo Quattropani, thesis title: ``Mixing and cover time on sparse random digraphs”, online presence, Rome, Italy, April 27, 2020; PhD defense of Janusz Meylahn, thesis title: ``Stochastic resetting and hierarchical synchronization'', Leiden, The Netherlands, September 24, 2019; PhD defense of Hakan Guldas, thesis title: ``Exploration on and of Networks", Leiden, The Netherlands, July 3, 2019; PhD defense of Andrea Roccaverde, thesis title: ``Breaking of ensemble equivalence for complex networks'', Leiden, The Netherlands, December 5, 2018; PhD defense of Andreas Stein Bethuelsen, thesis title: ``Random walks and the contact process'', Leiden, The Netherlands, November 22, 2016; PhD defense of Willem van Zuijlen, thesis title:``Gibbs-non-Gibbs transitions and vector-valued integration'', Leiden, The Netherlands, September 07, 2016; PhD defense of Herman Blok, thesis title: ``Unbounded-rate Markov decision processes: structural properties via a parametrisation approach'', Leiden, The Netherlands, June 23, 2016; PhD defense of Conrado Freitas Paulo da Costa, thesis title:``From reaction-diffusion models to the study of stochastic differential equations'', IMPA, Rio de Janeiro, Brazil, March 18, 2016; PhD defense of Renato Soares dos Santos, thesis title: ``Some case studies of random walks in dynamic random environments'', Leiden, The Netherlands, December 19, 2012

Master exams committees: DIMAI, Florence, for the following master students: Pietro Lotti (October 18, 2023); MI, Leiden, for the following master students: Sam Melief (October 6, 2021), Eduard Bosch (June 8, 2021), Josefien Verschuure (September 11, 2018), Lianne van der Velde (July 5, 2017), Vaya Sapobi Samui Vos (December 20, 2016), Giulia Pederzani (May 12, 2016), Dylan Gonzalez Arroyo (January 22, 2016).

9 Languages

Italian (mother tongue)

Dutch

English

Portuguese

Spanish

Luca AVENA

Interest

AREAS: Probability theory, statistical physics and complex networks.

TOPICS: Markov chains, random walks, self-avoiding walks, branching random walks, random media, disordered systems, interacting particle systems, hydrodynamic limits, large deviations, metastability, spectral geometry, random graph ensembles, random partitioning, random spanning trees and forests, FK-percolation, networks renormalization, randomized algorithms for network analysis.

BRIEF DESCRIPTION:My scientific production is constituted by two main lines of investigation I am developing along the years: the first line is fundamental and concerns the study of the long term behaviour of key models of random processes in random environments in different geometrical settings (integer lattices, non-regular graphs and random graphs, possibly changing over time), the second line is more applied and aims at designing randomized algorithms to analyze network based data sets by using random walk kernels and random rooted forests.