Graphon particle system: Uniform-in-time concentration bounds

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.

28 pages; revised Sections 1 and 2

References in corpus (5)

• Linear Quadratic Graphon Field Games
• Weakly interacting oscillators on dense random graphs
• Graphon mean field systems
• A note on Fokker-Planck equations and graphons
• Mean field interaction on random graphs with dynamically changing multi-color edges