Graphon particle system: Uniform-in-time concentration bounds

TL;DR

This paper develops uniform-in-time concentration bounds for graphon particle systems with heterogeneous interactions, providing finite and infinite time horizon estimates for the Wasserstein distance between empirical measures and their limits, extending prior work.

Contribution

It introduces new uniform-in-time concentration bounds for graphon particle systems with heterogeneous interactions, extending existing results to broader settings.

Findings

Established uniform-in-time concentration bounds for finite particle systems.

Extended concentration estimates to infinite time horizons.

Provided theoretical guarantees for Wasserstein distance convergence.

Abstract

In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite particle approximations. Under suitable growth (resp. convexity) assumptions, we obtain uniform-in-time concentration estimates, over finite (resp. infinite) time horizon, for the Wasserstein distance between the empirical measure and its limit, extending the work of Bolley--Guillin--Villani.