4.6 Article

On the Size of Chaos via Glauber Calculus in the Classical Mean-Field Dynamics

期刊

COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 382, 期 1, 页码 613-653

出版社

SPRINGER
DOI: 10.1007/s00220-021-03978-3

关键词

-

资金

  1. CNRS-Momentum program

向作者/读者索取更多资源

This study analyzes a system of classical particles and provides sharp estimates on many-particle correlation functions. By proposing a novel non-hierarchical approach, the BBGKY hierarchy can be truncated to any precision on the mean-field timescale, thereby justifying the Bogolyubov corrections to mean field. As a result, a quantitative central limit theorem for fluctuations of the empirical measure is derived, and the Lenard-Balescu limit for a spatially homogeneous system away from thermal equilibrium is discussed.
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 discrete stochastic calculus with respect to initial data in form of higher-order Poincare 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 discuss the Lenard-Balescu limit for a spatially homogeneous system away from thermal equilibrium.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.6
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据