A note on uniform in time mean-field limit in graphs
Résumé
In this article we wish to show, in a concise manner, a result of uniform in time propagation of chaos on random graphs. To do so, we combine the approaches of Delattre, Giacomin and Lu\c{c}on and of Durmus, Eberle, Guillin and Zimmer. In the case of a particle system interacting according to a graph, with a suitable scaling parameter and within a random environment, we use a coupling method suggested by Eberle known as reflection coupling to obtain a quantitative and uniform in time mean-field limit, provided the interaction is Lipschitz continuous and the restoring force satisfies a general one-sided Lipschitz condition (thus allowing for non-convex confining potential).