Large-scale concentration and relaxation for mean-field Langevin particle systems
Abstract
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for the modulated free energy functional. These properties yield near-optimal large-scale concentration and relaxation rates for the particle system throughout the subcritical regime. Furthermore, we derive generation of chaos estimates with the optimal order of particle approximation. As a simpler instance, we demonstrate long-time convergence of the independent projection of Langevin dynamics.
Keywords
Cite
@article{arxiv.2508.16428,
title = {Large-scale concentration and relaxation for mean-field Langevin particle systems},
author = {Songbo Wang},
journal= {arXiv preprint arXiv:2508.16428},
year = {2026}
}
Comments
59 pages; added Proposition 12 on uniform-in-time propagation of chaos for the supercritical Curie-Weiss model, along with other minor changes