01/10/2025, 17:00 — 18:00 — Online
Katharina Schuh, Technische Universität Wien
Long-time analysis of second-order Langevin diffusions with distribution-dependent forces and their numerical discretizations
In this talk, we explore the long-time behaviour of both the classical second-order Langevin diffusion and a non-linear variant with distribution-dependent forces of McKean-Vlasov type. In addition, we study a class of kinetic Langevin sampler – numerical discretization schemes for these continuous dynamics – and investigate their asymptotic behaviour.
We establish $L^1$ Wasserstein contraction for both the continuous dynamics and its numerical approximations using couplings and provide qualitative error bounds for the proposed numerical schemes. In our analysis, we consider not only strongly convex confining potentials but also multi-well potentials and non-gradient-type external forces as well as non-gradient-type interaction forces that can be attractive or repulsive.
For the non-linear variant, we exploit the connection to the corresponding particle system and we present a uniform in-time propagation of chaos result in $L^1$ Wasserstein distance.
