2024/05/29 by Armand Bernou, Bernou, Armand, Mitia Duerinckx +1 · 2 citations
Mathematics · Physics and Astronomy · #35Q70 #60F05 #60H07 #60K35 (Primary) 35Q84 #82C22 #82C31 (Secondary) #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2405.19306
openalex publication_date 2024/05/29 · openalex created_date 2024/05/31 · openalex updated_date 2026/07/30
We consider a system of classical Brownian particles interacting via a smooth long-range potential in the mean-field regime, and we analyze the propagation of chaos in form of sharp, uniform-in-time estimates on many-particle correlation functions. Our results cover both the kinetic Langevin setting and the corresponding overdamped Brownian dynamics. The approach is mainly based on so-called Lions expansions, which we combine with new diagrammatic tools to capture many-particle cancellations, as well as with fine ergodic estimates on the linearized mean-field equation, and with discrete stochastic calculus with respect to initial data. In the process, we derive some new ergodic estimates for the linearized Vlasov-Fokker-Planck kinetic equation that are of independent interest. Our analysis also leads to a uniform-in-time quantitative central limit theorem and to uniform-in-time concentration estimates for the empirical measure associated with the particle dynamics.