Uniform-in-\({N}\) Log-Sobolev Inequality for the Mean-Field Langevin Dynamics with Convex Energy
Abstract
Abstract. We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles [Formula: see text]. Our proof proceeds by establishing the existence of a Lipschitz transport map from the standard Gaussian measure via the reverse heat flow of Kim and Milman.
Fields of Study & Subjects
Markov Chains and Monte Carlo Methods
Random Matrices and Applications
Statistical Methods and Inference
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 4
- Pages
- 3652–3668
- Publication date
- 23 July 2026
- Language
- EN