This analysis demonstrates convergence of empirical distribution for kinetic particles influenced by Brownian motion, implying insights on non-linear PDE behavior.
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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Bellingeri et al. (2025) studied this question.
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