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

Understand

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 $L^1$ Wasserstein distance with an explicit dimension-free rate for pairwise weak interactions.
• For external forces corresponding to a $\kappa$-strongly convex potential, a contraction rate of order $\mathcal{O}(\sqrt{\kappa})$ is obtained in certain cases.
• But the contraction result is not restricted to these forces.