Carlo Bellingeri (Université de Haute-Alsace) -- A Law of Large Numbers for Kinetic Diffusions

mercredi 11 mars 2026, 10:30 → 11:30 Europe/Paris

In this talk, I will discuss a system of kinetic stochastic differential equations in which each particle is additively perturbed by a Brownian motion. In the deterministic setting, no assumptions are required beyond the convergence of the empirical measure. By contrast, the stochastic framework typically requires either strong exchangeability of the initial particle configuration or certain technical moment assumptions to study the convergence of the empirical measure. Using a family of anisotropic Sobolev spaces, a “simple” SPDE satisfied by the empirical measure, and the Garsia–Rodemich–Rumsey lemma, I will show how one can recover a result similar to the deterministic framework and establish a classical law of large numbers for kinetic diffusions.