Mean-field approximation, Gibbs relaxation, and cross estimates
While it is known that propagation of chaos holds at rate $O(1/N)$ uniformly in time, and Gibbs relaxation at rate $O(e^{-ct})$ uniformly in $N$, we go a step further by showing that the cross error between chaos propagation and Gibbs relaxation is $O(N^{-1}e^{-ct})$.
Jul 31, 2025
Uniform-in-time estimates on corrections to mean field for interacting Brownian particles
We analyze the propagation of chaos of a mean-field system of classical Brownian particles interacting via a smooth long-range potential in form of uniform-in-time estimates with optimal N-dependence on many-particle correlation functions. The kinetic Langevin setting and the overdamped Brownian dynamics are covered.
May 23, 2025
Creation of chaos for interacting Brownian particles
We establish a fine version of the so-called creation-of-chaos phenomenon':' in weak norms, the mean-field approximation for a typical particle is shown to hold with an accuracy O(1/N) up to an error due solely to initial pair correlations.
Apr 14, 2025