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

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. We establish global contraction in an L 1 -Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions. The contraction result is not restricted to external forces corresponding to strongly convex confining potentials. It rather includes multi-well potentials and non-gradient-type external forces as well as non-gradient-type repulsive and attractive interaction forces. In the proof, we use a coupling approach and construct a distance function adjusted to it. By applying a componentwise adaptation of the coupling we obtain uniform in time propagation of chaos bounds for the corresponding mean-field particle system. The talk is based on arXiv :2206.03082.