Probability Seminar

Speaker: Nguyen, Hung Dang

Affiliation: University of Tennessee Knoxville

Abstract:  We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori-Zwanzig approach, we represent the GLE by a system of SDEs and investigate the large-time stability of the Markov dynamics. Under a general set of conditions on the nonlinearities, we demonstrate that the Markov GLE is always exponentially attractive toward the unique invariant Gibbs measure. Important examples of singular potentials in our results include the Lennard-Jones function and the Coulomb function.

Title: Ergodicity of the generalized Langevin equation with singular potentials