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

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 (2016) known as reflection coupling to obtain uniform in time mean-field limit with bounds that depend explicitly on the graph structure.