Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials

Abstract

AbstractWe study Langevin dynamics of N particles on ℝd interacting through a singular repulsive potential, e.g., the well‐known Lennard‐Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. © 2019 Wiley Periodicals, Inc.