Schuh, K. J. (2023, June 14). Global contractivity for Langevin dynamics with distribution-dependent forces and uniform in time propagation of chaos [Conference Presentation]. Summer school - Mean field models 2023, Rennes, France.
Langevin dynamics; Vlasov-Fokker-Planck equation; propagation of chaos; coupling
en
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.
