A note on uniform in time mean-field limit in graphs

TL;DR

This paper demonstrates uniform in time propagation of chaos for particle systems on graphs with Lipschitz interactions, using reflection coupling, and provides bounds depending on the graph structure.

Contribution

It extends mean-field limit results to non-exchangeable particle systems on dense graphs with non-convex potentials, using a reflection coupling approach.

Findings

Uniform in time propagation of chaos established.

Explicit bounds depending on graph density derived.

Applicable to systems with non-convex confining potentials.

Abstract

In this article we show, in a concise manner, a result of uniform in time propagation of chaos for non exchangeable systems of particles interacting according to a random graph. Provided the interaction is Lipschitz continuous, the restoring force satisfies a general one-sided Lipschitz condition (thus allowing for non-convex confining potential) and the graph is dense enough, we use a coupling method suggested by Eberle known as reflection coupling to obtain uniform in time mean-field limit with bounds that depend explicitly on the graph structure.