Uniform-in-time estimates on corrections to mean field for interacting Brownian particles

• 成果类型: Article; Early Access
• 署名作者: Bernou, Armand; Duerinckx, Mitia
• 署名单位: Universite Claude Bernard Lyon 1; Universite Libre de Bruxelles
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01381-w
• 发表日期: 2025
• 关键词: fokker-planck equation; self-stabilizing processes; granular media equations; Wasserstein Distance; kinetic-equations; propagation; CONVERGENCE; chaos; inequalities; equilibrium

摘要

We consider a system of N 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 uniform-in-time estimates with optimal N-dependence 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 concentration estimates for the empirical measure associated with the particle dynamics.