Global contractivity for Langevin dynamics with distribution-dependent forces and uniform in time propagation of chaos

2022/06/07 by Katharina Schuh, Schuh, Katharina · 9 citations
Mathematics · Physics and Astronomy · #60H10 #60J60 #82C31 #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.2206.03082

openalex publication_date 2022/06/07 · openalex created_date 2022/06/13 · openalex updated_date 2026/08/01

Abstract

We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish global contraction in an L¹ Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions. For external forces corresponding to a κ-strongly convex potential, a contraction rate of order O(√κ) is obtained in certain cases. But the contraction result is not restricted to these forces. It rather includes multi-well potentials and non-gradient-type external forces as well as non-gradient-type repulsive and attractive interaction forces. The proof is based on a novel distance function which combines two contraction results for large and small distances and uses a coupling approach adjusted to the distance. By applying a componentwise adaptation of the coupling we provide uniform in time propagation of chaos bounds for the corresponding mean-field particle system.

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