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arXiv · 2508.16428

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

Songbo Wang
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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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Songbo Wang. 2026-05-27. Large-scale concentration and relaxation for mean-field Langevin particle systems. https://arxiv.org/abs/2508.16428

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