Concentration of measure for Graphon particle system

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.

References in corpus (4)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Graphon Mean Field Games and the GMFG Equations
• A note on dynamical models on random graphs and Fokker-Planck equations
• A note on Fokker-Planck equations and graphons

Cited by in corpus (1)

• An Overview of Some Extensions of Mean Field Games beyond Perfect Homogeneity and Anonymity