Table des matières

Research

Main research topics

Biological systems:

  • Synchronization phenomena
  • Link between biological models and nonequilibrium statistical mechanics.

Disordered systems:

  • Random walks in random media
  • Interfaces and directed polymer models
  • Stochastic billiards
  • Pinning models
  • Waves in random media
  • Mirrors model
  • Deterministic walk in random environment

Large deviations:

  • First passage percolation
  • Kinetically constrained models
  • Renewal processes
  • Numerical methods and algorithms

Nonequilibrium statistical mechanics:

  • Transport in interacting particle systems
  • Fourier law in extended systems
  • Hydrodynamic limit
  • Spectral gap
  • Dynamical phase transitions
  • Ergodicity breaking in glass models

Networks, trees and random graphs:

  • Dynamics on stochastic networks
  • Coagulation and gelation dynamics and self-organized criticality

Random matrices and algebraic structures in statistical physics:

  • Eigenvalues and eigenvectors of random matrices
  • Dimer models
  • Exactly solvable models

Stochastic processes:

  • Invariant measure of models subjected to random perturbations
  • Random walks and Brownian motion on groups
  • Probabilistic interpretation of partial differential equations
  • Discretization of stochastic differential equations
  • Cover time and cover process
  • Random interlacements

Projects

ERC MALIG: A mathematical approach to the liquid-glass transition: kinetically constrained models, cellular automata and mixed order phase transitions
Coordinator: Cristina Toninelli
Member : Aurélia Deshayes, Vivien Lecomte

ANR PPPP: Percolation et Percolation de Premier Passage
Members : Aurélia Deshayes, Marie Théret

ANR SAMARA: Spectres, Algorithmes et Marches Aléatoires dans les Réseau Aléatoires
Membres : Justin Salez, Pierre Youssef

ANR LSD: Large Stochastic Dynamical Models in Non-Equilibrium Statistical Physics
Membres : Giambattista Giacomin, Vivien Lecomte, Raphaël Lefevere, Cristina Toninelli

Math-AmSud: Large-scale behavior of stochastic systems
Membres : Francis Comets, Cristina Toninelli