2025/04/25 by Axel Ringh, Akash Sharma, Ringh, Axel +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q84 #37H10 #60H10 #60H35 #65C30 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics and Entropy #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2504.18139
openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and inverse problems using Kalman techniques - results in a mean-field (McKean-Vlasov) SDE. We demonstrate exponential convergence of the time marginal law of the mean-field SDE to the Gibbs measure with non-Gaussian potentials. This extends previous results, obtained in the Gaussian setting, to a broader class of potential functions. We also establish uniform in time bounds on all moments and convergence in p-Wasserstein distance. Furthermore, we show convergence of a weak particle approximation, that avoids computing the square root of the empirical covariance matrix, to the mean-field limit. Finally, we prove that an explicit numerical scheme for approximating the particle dynamics converges, uniformly in number of particles, to its continuous-time limit, addressing non-global Lipschitzness in the measure.