Interacting particle systems*

Abstract

We present in this paper a number of recent and various works of statistical physics, which involve an interacting particle system. In kinetically constrained models, the particles are placed on ℤd, with local constraints on the dynamics, that can slow down the evolution and reproduce the behaviour of glassy systems. The contact process (or Suspected-Infected-Susceptible) is a simple model for the spread of an infection on a (general) graph. In the Kuramoto model, the motion of the particles is determined by a diffusion system with mean-field interaction. Finally, in the modeling of the vertex reinforced jump process (a particle that interacts with itself via its path), we show an unexpected link with an interacting particle system.