Ninon Fétique (Université de Tours)

Title: Stochastic billiard in a convex set

Abstract: We consider the following dynamic: a particle moves at unit speed inside a convex set until it hits its boundary. At this time, the particle is reflected inside the domain according to a random distribution, not depending on its position and its previous velocity. The pair (location,velocity) of this particle is a continuous-time Markov process, and the successive locations of hitting points on the boundary are a Markov chain. We are interested in the speeds of convergence of these two processes towards their invariant measures. We will therefore describe a coupling that gives explicit upper bounds for these speeds of convergence, in some particular cases for the convex in which the stochastic billiard evolve.