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Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials
Author(s) -
Herzog David P.,
Mattingly Jonathan C.
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21862
Subject(s) - mathematics , ergodicity , langevin dynamics , invariant measure , lyapunov function , convergence (economics) , invariant (physics) , statistical physics , mathematical analysis , ergodic theory , mathematical physics , physics , quantum mechanics , nonlinear system , statistics , economics , economic growth
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.