On uniform in time propagation of chaos

Abstract

Propagation of chaos is a phenomenon according to which, in a system of N interacting particles, two given particles become « more and more » independent as N goes to infinity. Proving such a phenomenon, with hopefully a quantitative rate, allows one to boil down the study of large systems of particles to the study of a single (non-linear) PDE, thus going from a microscopic model to a mesoscopic one. Obtaining uniform in time results, i.e understanding how this convergence in N evolves with time, is then an important problem in practice, and strongly linked to the long-time behavior of the various models. During this talk, I will be discussing some recent results and methods. It will contain some joint works with A. Guillin et P. Monmarché as well as with L. Journel.