A law of large numbers for kinetic interacting diffusions

2025/06/02 by Bellingeri, Carlo, Coppini, Fabio
#60F05 #60H20 #60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.01769

Abstract

We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial differential equations. Under general assumptions that require only weak convergence on the initial datum -- without assuming independence or moment conditions -- we prove convergence in probability to the corresponding non-linear Fokker-Planck PDE.

Citations

• Sobolev embeddings for kinetic Fokker-Planck equations
• Singular kinetic equations and applications
• Cauchy Problem of Stochastic Kinetic Equations
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• Large-time behaviour for coupled systems of Lotka-Volterra-type Fokker-Planck equations