Probability Seminar

Date: November 4, 2020

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Maria Gordina, University of Connecticut

Title: Ergodicity for Langevin dynamics with singular potential

Abstract: We discuss Langevin dynamics of N particles on R^d interacting through a singular repulsive potential, such as the Lennard-Jones potential, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted Sobolev norm. The proof relies on an explicit construction of a Lyapunov function using a modified Gamma calculus. In contrast to previous results for such systems, our results imply geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. This is based on the joint work with F. Baudoin and D. Herzog.