Quantum mechanics

Ergodicity

Mathematical physics

Statistics

Dynamics (music)

Applied mathematics

Convergence (economics)

Economics

Acoustics

Statistical physics

Langevin dynamics

Physics

Nonlinear system

Mathematics

Invariant (physics)

Lyapunov function

Mathematical analysis

Invariant measure

Economic growth

Ergodic theory

Communications on Pure and Applied Mathematics

We study Langevin dynamics of N particles on ℝ d 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.

Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials