Schuh, K. J. (2024, September 18). Global contractivity for Langevin dynamics with distribution-dependent forces via couplings [Conference Presentation]. Large scale behaviour of interacting diffusions, Italy.
We analyse the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. After giving a short recap on coupling methods we introduce a coupling approach to establish global contraction in an L₁ Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions. For external forces corresponding to aκ-strongly convex potential, a contraction rate of order O(√k) is obtained in certain cases. But, the contraction result is not restricted to these external 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 construction adjusted to the distance. By applying a componentwise adaptation of the coupling we can prove uniform in time propagation of chaos bounds for the corresponding mean-field particle system.