Abstract: I will talk about the mixing time which is the time it takes for a random walk to reach equilibrium. My focus will be on the cutoff phenomenon observed when the transition to equilibrium happens abruptly in time. I will survey the developments in the last 30 years and present a recent universality result for graphs with a random matching that was obtained in collaboration with J. Hermon and A. Sly.

Laurent Miclo
Title: On set-valued intertwining duality for Markov processes

Abstract: In the introductory talk, we present the classical Markov intertwining relations developed by Diaconis and Fill in the finite state space setting. They provide a probabilistic approach to convergence to equilibrium via strong stationary times and separation discrepancy.
In the second talk, we will see how to adapt this method to diffusions on Riemannian manifolds, via stochastic extensions of mean curvature flows (based on works with Arnaudon and Koulibaly).