Tue, May 4, 2021, 12:30 pm
Title: Trend to equilibrium for log-Coulomb gases for non-convex external potentials
Abstract: It is well known that the eigenvalues of some random matrices behave like stochastic interacting particles under an external potential. After recalling those facts, we will consider the generalized Dyson Brownian motion. When the number of particles goes to infinity, the empirical measure of the system satisfies a Fokker-Planck equation. We are interested in the asymptotic behavior of the solution. It has been proved that when the potentials are convex, the solution converges in the Wasserstein space W_2 to the minimizer of an entropy. We extend this to some non-convex potentials using functional inequalities.