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Title: Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
Speaker: David Herzog (Iowa State University)
Time: Friday, November 16, 2018 at 1:30 pm
Place: MONT 313Abstract: We discuss 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 result turns 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.