A law of large numbers for kinetic interacting diffusions

Carlo Bellingeri; Fabio Coppini

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arXiv · 2506.01769

A law of large numbers for kinetic interacting diffusions

Carlo Bellingeri·Fabio Coppini

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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.

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Carlo Bellingeri, Fabio Coppini. 2025-06-02. A law of large numbers for kinetic interacting diffusions. https://arxiv.org/abs/2506.01769

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