An Elementary Approach To Uniform In Time Propagation Of Chaos

TL;DR

This paper introduces a coupling-based method to establish uniform in time propagation of chaos for mean-field particle systems, accommodating non-convex potentials and providing explicit bounds.

Contribution

It presents a novel coupling approach combining reflection and synchronous couplings to handle non-convex potentials, extending previous convex case results.

Findings

Proves uniform in time propagation of chaos for non-convex potentials.

Provides explicit quantitative bounds for the particle systems.

Extends previous results from convex to non-convex interaction potentials.

Abstract

Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of reflection and synchronous couplings applied to the individual particles. It provides explicit quantitative bounds that significantly extend previous results for the convex case.