Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 382, Issue 1, Pages 613-653Publisher
SPRINGER
DOI: 10.1007/s00220-021-03978-3
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- CNRS-Momentum program
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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.
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