Sharp uniform-in-time propagation of chaos

• 成果类型: Article; Early Access
• 署名作者: Lacker, Daniel; Le Flem, Luc
• 署名单位: Columbia University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-023-01192-x
• 发表日期: 2023
• 关键词: granular media equations; mean-field limit; systems; inequalities; DYNAMICS; MODEL

摘要

We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that the distance between the k-particle marginal of the n-particle system and its limiting product measure is O((k/n)(2)), uniformly in time, with distance measured either by relative entropy, squared quadratic Wasserstein metric, or squared total variation. Our proof is based on an analysis of relative entropy through the BBGKY hierarchy, adapting prior work of the first author to the time-uniform case by means of log-Sobolev inequalities.