2019/12/03 by Mitia Duerinckx, Duerinckx, Mitia · 4 citations
Mathematics · Physics and Astronomy · #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 #Theoretical and Computational Physics #math-ph #math.AP #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1912.01366
38 pages
openalex publication_date 2019/12/03 · arxiv created 2021/11/29 · arxiv updated 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a system of classical particles, interacting via a smooth, long-range potential, in the mean-field regime, and we optimally analyze the propagation of chaos in form of sharp estimates on many-particle correlation functions. While approaches based on the BBGKY hierarchy are doomed by uncontrolled losses of derivatives, we propose a novel non-hierarchical approach that focusses on the empirical measure of the system and exploits a Glauber type calculus with respect to initial data in form of higher-order Poincaré inequalities for cumulants. This main result allows to rigorously truncate the BBGKY hierarchy to an arbitrary precision on the mean-field timescale, thus justifying the Bogolyubov corrections to mean field. As corollaries, we also deduce a quantitative central limit theorem for fluctuations of the empirical measure, and we partially justify the Lenard-Balescu limit for a spatially homogeneous system away from thermal equilibrium.