Recent Work

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Books

• Markov Chains on Metric Spaces. A short Course (with Tobias Hurth)

Springer, Universitext, 2022,

• Promenade Aléatoire ; Chaînes de Markov et Simulations, martingales et stratégies (with Nicole El Karoui)

Les éditions de l’école Polytechnique, 2005

Preprints

• The asymptotic behavior of fraudulent algorithms (with Laurent Miclo)
• Regularity of the stationary density for systems with fact random switching (with Oliver Tough)
• Degenerate processes killed at the boundary of a domain (with Nicolas Champagnat, William Oçafrain, and Denis Villemonais)
• Stochastic Persistence
• On strict convergence of stochastic gradients

Papers

• A note on the top Lyapunov exponent of linear cooperative systems (with Claude Lobry, Tewfik Sari and Edouard Strickler)

Annales de la Faculté des Sciences de Toulouse, Accepted.

• When can a population spreading across sink habitats persist ? (with Claude Lobry, Tewfik Sari and Edouard Strickler)

Journal of Mathematical Biology, 2024 88:19.

• Untangling the role of temporal and spatial variations in persistence of populations (with Claude Lobry, Tewfik Sari and Edouard Strickler)

Theoretical population biology, 154, 2023, 1-26

• Stochastic persistence in degenerate stochastic Lotka-Volterra food chains (with Antoine Bourquin and Dang H Nguyen)

Discrete and Continuous Dynamical Systems - B, 2022, Vol 27, No 11, 6841-6863

• Transcritical bifurcation for the conditional distribution of a diffusion process (with Nicolas Champagnat, William Oçafrain, and Denis Villemonais)

Journal of Theoretical Probability, 2022

• Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain (with Nicolas Champagnat and Denis Villemonais)

Annales de l'Institut Henri Poincaré, 2021, Vol 57, No 2, 726-739

· Analysis of an Adaptive Biasing Force method based on self-interacting dynamics (with Charles-Edouard Bréhier and Pierre Monmarché )

Electronic Journal of Probability, Vol 25, 2020

· Persistence and extinction for stochastic ecological difference equations with feedbacks (With Sebastian Schreiber )

Journal of Mathematical Biology, 2019.

• Convergence analysis of Adaptive Biasing Potential methods for diffusion processes (with Charles-Edouard Bréhier)

Communications in Mathematical Science, Vol 17, 2019, pp 81-130.

• Random Switching between vector fields having a common equilibrium (with Edouard Strickler)

Annals of Applied Probability, 2019, Vol. 29, No. 1, 326-375

• Stochastic approximation of quasi-stationary distributions on compact spaces and applications (with Bertrand Cloez and Fabien Panloup)

Annals of Applied Probability, 2018, Vol. 28, No 4, 2370-2416.

• A user-friendly condition for exponential ergodicity in randomly switched environments (with Tobias Hurth and Edouard Strickler)

Electronic Communications in Probability, 2018, Vol. 23

• Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories (with Florian Bouguet and Bertrand Cloez )

Annals of Applied Probability, 2017, Vol. 27, No 5, 3004-3049.

· Supports of Invariant Measures for Piecewise Deterministic Markov Processes (with Fritz Colonius and Ralph Lettau)

Nonlinearity, 2017, Vol 30, No 9, 3400-3418

• Self-repelling diffusions on a Riemannian manifold (with Carl-Erik Gauthier)

Probability Theory and Related Field, 2016, https://doi.org/10.1007/s00440-016-0717-1

• Lotka Volterra in fluctuating environment or "how switching between beneficial environments can make survival harder (with Claude Lobry)

Annals of Applied Probability, 2016, Vol 26, No 6, 3754-3785

· Convergence of Adaptive Biasing Potential methods for diffusions (with Charles-Edouard Bréhier)

Comptes rendus Mathématiques (comptes rendus de l’Académie des Sciences, Série I) 2016, Vol 354, Issue 8, 842-846

• Smale Strategies for Network Prisoner’s Dilemma Games (with Kashi Behrstock and Morris W Hirsch)

Journal of Dynamics and Games, Vol 2, No 2, pp 141-155, 2015

• Self-repelling diffusions via an infinite dimensional approach (with Iona Ciotir and Carl-Erik Gauthier)

Stochastic Partial Differential Equations: Analysis and Computation, 2015 Volume 3, Issue 4, Pages 506-530

• On Gradient like properties of Population games, Learning models and Self Reinforced Processes

“Dynamics, Games and Science, DGS II” Springer-Verlag (J.P Bourguignon, R. Jelstch, A. Pindo and M. Viana, eds) CIM Series in Mathematical Sciences, 117-152, 2015

• A Stochastic Approximation Approach To Quasi-Stationary Distributions on Finite Spaces (with Bertrand Cloez )

Electronic Communications in Probability, Vol 20, 1-14, 2015

• Qualitative properties of certain piecewise deterministic Markov processes (with Stéphane Le Borgne, Florent Malrieu and Pierre-André Zitt)

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques Volume 51, Number 3, 1040-107, August 2015.

Erratum, 2018

• A Generalized Polya’s urn with graph based interaction (With Itai Benjamini, Jun Chen and Yuri Lima)

Random Structures and Algorithms Volume 46, Issue 4, Pages: 614–634, July 2015.

• On the stability of planar randomly switched systems (with Stéphane Le Borgne, Florent Malrieu and Pierre-André Zitt)

Annals of Applied Probability. Vol 24, Number 1, 292-311, 2014,

• Consistency of Vanishingly smooth fictitious play (with Mathieu Faure)

Mathematics of Operation Research,. Vol 38, Number 3, 437-450, 2013

• Strongly Reinforced Vertex-Reinforced Random Walks on the Complete Graph (With Bruno Schapira and Olivier Raimond)

ALEA Lat. Am.. J. Probab Math. Stat. 10 (2013), 2, 767-782

• Quantitative ergodicity for some switched dynamical systems (with Stéphane Le Borgne, Florent Malrieu and Pierre-André Zitt)

Electronic Communications in Probability, Vol 17, 1-14, 2012

• Perturbations of set-valued dynamical systems with applications to game theory (With  Josef Hofbauer and Sylvain Sorin ). 

Dynamics, Games and Applications. 2, 195-205, (2012)

• Stochastic approximations, Cooperative Dynamics and Supermodular Games (with Mathieu Faure)

The Annals of Applied Probability. Volume 22, Number 5 (2012), 2133-2164.

• Self-interacting diffusions IV: Rate of convergence (With Olivier Raimond ).

Electronic Journal of Probability Vol. 16 (2011), Paper no. 66, pages 1815–1843.

• Dynamics of Vertex-Reinforced Random Walks . (With Pierre Tarres)

Annals of Probability, 2011, Vol. 39, No. 6, 2178–2223

• A class of self interacting processes with applications to games and reinforced random walks (With Olivier Raimond ).

Siam Journal on Control and Optimization, 2010. Vol. 48, No. 7, pp. 4707–4730

• Persistence in fluctuating environments (With Sebastian Schreiber and Kolawolé Atachadé)

Journal of Mathematical Biology, 2010.

• Persistence of structured populations in random environments. (With Sebastian Schreiber )

Theoretical Population Biology, 76 (2009), 19-34

• Learning in games with unstable equilibria. (With  Josef Hofbauer and Ed Hopkins ) .

Journal of Economic Theory, 144 (2009), 1694-1709

• A class of mean field interaction models for computer and communication systems (With  Jean Yves Le Boudec )

Performance Evaluation, 2008, Vol 65, Issues 11-12, 823-838

• Exponential concentration for first passage percolation through modified Poincaré inequalities (With  Raphael Rossignol ). 

Annales de l'Institut Henri Poincaré, 2008, Vol 44, No3, 544-573.

• A modified Poincaré inequality and its application to First Passage Percolation (With  Raphael Rossignol ).
• Robust Permanence and Impermanence for the Stochastic Replicator Dynamics (With  Josef Hofbauer and Bill Sandholm ). 

Journal of Biological Dynamics, Vol 2, No 2, April 2008, 180-195.

• A Bakry-Emery criterion for self-interacting diffusions. (With Olivier Raimond ). 

Progress in Probability (proceedings of the fifht conference on stochastic analysis, random field and applications), Vol 59, 19-22, 2007.

• Un joli problème d'Erdös.
  Images du CNRS 2006 .
  
  
• Stochastic Approximations and Differential Inclusions II: Applications. (With  Josef Hofbauer and Sylvain Sorin ). 

Mathematics of Operation Research Vol 31, N0. 4, November 2006.

• Self Interacting Diffusions III: Symmetric Interactions. (With Olivier Raimond ). 

Annals of Probability. Vol 33, (2005), No. 5, 1716-1759

• Stochastic Approximations and Differential Inclusions. (With  Josef Hofbauer and Sylvain Sorin ).
  SIAM Journal on Control and Optimization. Vol. 44, (2005), No 1, pp. 328-348
• Generalized Urn Models of Stochastic Evolution. (With Sebastian Schreiber and Pierre Tarres).

Annals of Applied Probability. 14, (2004), no 3 1455--1478.

• A Two Armed Type Bandit Problem. (With Gerard Ben-Arous ).

International Journal of Game Theory. 32 (2003), no 1, 3--16.

• Deterministic Approximation of Stochastic Evolution in Games (With Jorgen Weibull ).

Econometrica. (2003), 71, 3 873-903

• Self Interacting Diffusions II: Convergence in Law. (With Olivier Raimond ).

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. (2003), 6, 1043-1055.

• On Self Attracting/ Repelling Diffusions. (With Olivier Raimond ).

Comptes rendus de l' Académie des Sciences. (2002), I 335, 541-544.

• Self-Interacting Diffusions. (With Michel Ledoux and Olivier Raimond ).

Probability Theory and related Fields. (2002), Vol 122, 1, 1-44.

• Metric Properties of the Group of Area Diffeomorphisms. (With Jean Marc Gambaudo ).

Transactions of the A.M.S. (2001), Vol 353, 11, 4661-4672

• Standardization in Decentralized Economies. (With Emmanuelle Auriol ).

American Economic Review. (2000) Vol 90, No 3, pp 550-570

• Convergence and Oscillation in Standardization Games. (With Emmanuelle Auriol ).

European Journal of Economic and Social Systems. (2001) Vol 15, 1, pp 39-55.

• Weak Asymptotic Pseudotrajectories for Semiflows: Ergodic Properties. (With Sebastian Schreiber ).

Journal of Dynamics and Differential Equations. Vol 12, Number 3, 2000.

• Convergence with probability one of stochastic approximation algorithms whose average is cooperative.

Nonlinearity. Vol 13, pp 601-616, 2000.

• Stochastic Adaptive Behavior for Prisoner's Dilemma. (With Morris. W Hirsch ).

Preprint.

• Dynamics of Stochastic Approximations.

Le Seminaire de Probabilites. Lectures Notes in Mathematics, Vol 1709, pp 1-68.

• Stochastic Approximation Algorithms with Constant Step Size whose Average is Cooperative. (With Morris. W Hirsch ).

The Annals of Applied Probability. Vol 9, No 1, pp 216-241, 1999.

• Learning Processes, Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games. (With Morris. W Hirsch ).

Games and Economic Behavior. Vol 29, 36-72, 1999.

• Differential and Stochastic Epidemic Models. (With Morris. W Hirsch ).

The Fields Institute Communications. Volume 21, 1999

• Almost Sure Convergence of the One-Dimensional Kohonen Algorithm. (With Jean Claude Fort and Gilles Pages ).

Advances in Applied Probability. Vol 30, pp 850-869, 1998

• Recursive Algorithms, Urn Processes and Chaining Number of Chain Recurrent Sets.

Ergodic Theory and Dynamical Systems. 18, pp 53-87, (1998).

• On Invariant Hypersurfaces of Strongly Monotone Maps.

Journal of Differential Equations. Vol 137, No 2, pp 302-319, July 1, (1997)

• Vertex Reinforced Random Walks and a Conjecture of Pemantle.

The Annals of Probability. Vol 25, No 1, pp 361-392, (1997)

• A Dynamical System Approach to Stochastic Approximations.

SIAM J. Control and Optimization. Vol 34, No 2, pp 437-472, March (1996).

• Dynamics of Morse-Smale Urns Processes. (With Morris. W Hirsch ).

Ergodic Theory and Dynamical Systems. Vol 8, No 1, pp 141-174. (1996).

• Chain Recurrence in Surface Flows. (With Morris. W Hirsch ).

Discrete and Continuous Dynamic Systems. Vol 1, Number 1, pp 1-17. (1995)

• Asymptotic Pseudo-Trajectories and Chain-recurrent flows, with Applications. (With Morris. W Hirsch).

Journal of Dynamics and Differential Equations. Vol 8, No 1 pp 141-174. (1996).

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