Concentration of measure for Graphon particle system

TL;DR

This paper establishes exponential concentration bounds for the empirical measures of heterogeneously interacting particle systems modeled by graphons, extending previous mean-field results to more complex network structures.

Contribution

It provides new concentration estimates for finite particle systems approximating graphon-based mean-field models, advancing understanding of their probabilistic behavior.

Findings

Exponential concentration estimates for empirical measures.

Extension of Bayraktar-Wu's work to graphon interactions.

Quantitative bounds in Wasserstein distances.

Abstract

We study heterogeneously interacting diffusive particle systems with mean-field type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration estimates over a finite time horizon for both 1 and 2 Wasserstein distances between the empirical measures of the finite particle systems and the averaged law of the graphon system, extending the work of Bayraktar-Wu.