Probability and ergodic theory

Here are the main themes our group is currently working on.

Stochastic processes

  • Central Limit Theorem and Invariance Principle for random processes
  • Self similar random fields
  • Logarithmic Sobolev type inequalities and applications in probability theory
  • Piecewise deterministic Markov processes (projet ANR PIECE)
  • Stochastic models for population dynamics

Random walks: probabilistic and combinatorial aspects

  • Random walks and enumeration of walks in cones
  • Conditioned random walks in Weyl chambers and Pitman transform (projet académique MADACA)
  • Harmonic analysis and Dunkl Processes
  • Boundary theory (e.g., Martin boundary)
  • Branching random walks and Fisher-KPP equations

Statistical mechanics

  • Dimer models in statistical mechanics
  • Percolation and first-passage percolation (ANR PPPP)
  • Interacting particles systems

Ergodic theory, dynamical systems and ergodic geometry

  • Simple and multiple ergodic averages
  • Limit Theorems for dynamical systems
  • Szemeredi type recurrence properties
  • Limit theorem for the geodesic flow in negative curvature
  • Entropy and growth of volume of balls in negative curvature (GDR PLATON)
  • Combinatorial number theory