Large-scale concentration and relaxation for mean-field Langevin particle systems

2025/08/22 by Wang, Songbo
#60K35 (Primary) 60J60 #82C31 (Secondary) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.16428

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.

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