Recent Work

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(Text)Book

• Promenade Aléatoire . (With Nicole El Karoui ).                                        

Cours de l'Ecole Polytechnique

Preprints

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

To appear in Performance Evaluation

• A modified Poincaré inequality and its application to First Passage Percolation (With  Raphael Rossignol ).
• Learning in games with unstable equilibria. (With  Josef Hofbauer and Ed Hopkins ) . 

To appear in Journal of Economic Theory

• Simulated Annealing, Vertex-Reinforced Random Walks and Learning in Games. (With Olivier Raimond ).
• Persistence of structured populations in random environments . (With Sebastian Schreiber ).

To appear in Theoretical Population Biology

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

Recent papers

• 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.

• 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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