Ergodicity and propagation of chaos for mean field kinetic particles

TL;DR

This paper investigates the long-term behavior of large particle systems governed by Vlasov-Fokker-Planck equations with convex potentials, establishing uniform propagation of chaos and exponential convergence rates.

Contribution

It provides a quantitative analysis of ergodicity and propagation of chaos without smallness restrictions on interactions in mean field kinetic particles.

Findings

Uniform in time propagation of chaos estimates

Exponential convergence to equilibrium

Quantitative approach to ergodicity

Abstract

The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are derived uniform in time propagation of chaos estimates, which themselves yield in turn an exponentially fast convergence for the semi-linear equation itself. The approach is quantitative.