Long time behaviour and particle approximation of a generalized Vlasov dynamic

TL;DR

This paper studies a generalized Vlasov equation, providing quantitative convergence rates to equilibrium and demonstrating that a particle system approximates the equation with propagation of chaos.

Contribution

It introduces a quantitative convergence rate to the stationary solution and establishes a particle approximation with propagation of chaos for the generalized Vlasov dynamic.

Findings

Quantitative convergence rate in Wasserstein metric

Particle approximation satisfying propagation of chaos

Analysis of long-term behavior of the generalized Vlasov system

Abstract

In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly, we obtain a quantitative rate of convergence to the stationary solution in the Wasserstein metric. Secondly, we provide a many-particle approximation for the equation and show that the approximate system satisfies the propagation of chaos property.