2023/12/13 by Keunwoo Lim, Lim, Keunwoo, Molei Tao +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2312.07817
openalex publication_date 2023/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate position-dependent friction coefficient and the possible accelerated convergence it enables. We show that by choosing this coefficient matrix to be 2√(HessV), convergence is accelerated in the sense that no constant scalar friction coefficient can lead to faster convergence for a large subset of (nonlinear) strongly-convex potential V's. The speed of convergence is quantified in terms of chi-square divergence from the target distribution, and proved using a Lyapunov approach, based on viewing sampling as optimization in the infinite dimensional space of probability distributions.