Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases

Arnaud Guillin (1) , Pierre Le Bris (2) , Pierre Monmarché (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is (locally) Lipschitz continuous and the confining potential is both Lipschitz continuous and greater than a quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle adapted to the kinetic setting enabling also to obtain uniform in time propagation of chaos in a non convex setting.

Domaines: Probabilités [math.PR]

Arnaud Guillin, Pierre Le Bris, Pierre Monmarché. Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases. 2021. ⟨hal-03323156⟩