Laurent Miclo: On Markov intertwinings

Coffee: 15:30 - 16:00
 

Abstract: As the audience mainly belongs to the PDE community, we will begin by giving a feeling of Markov processes through the simple example of top-to-random card shuffle and by showing how the notion of strong stationary times enabled Aldous and Diaconis (1986) to study its quantitative convergence to equilibrium. The goal of the talk is to extend the underlying principle to elliptic diffusions on manifolds, via Markov intertwinings, which correspond to a weak similar relation between semigroups (preserving non-negativity and the function 1). Instead of only looking at the motion of one diffusive particle, we will couple it with dynamical domains containing the particle and whose boundary evolution is a stochastic modification of the mean curvature flows. The (remote) hope is a new probabilistic approach to Hörmander's theorem.