# Séminaire de Physique Mathématique, CPHT, Mercredi 11 mars 2020

**Salle de Conférence Louis Michel**

**14:00-15:00 : Bart van Ginkel**

**Title: Hydrodynamic limit of the Symmetric Exclusion Process on compact Riemannian manifolds.**

Abstract: In this talk I will first explain the concept of the hydrodynamic limit of an interacting particle system. The idea is that one wants to show that when both space and time are rescaled (appropriately), the limiting densities of particles satisfy some PDE. This will be illustrated with the Symmetric Exclusion Process. Then we move this basic particle system to a hard context: Riemannian manifolds. I will highlight which challenges arise in the curved setting and how we deal with them. Joint work with Frank Redig.

**15:00-16:00 : Rik Versendaal**

**Title: Large deviations for geodesic random walks.**

Abstract: The theory of large deviations is concerned with the limiting behaviour on the exponential scale of a sequence of random variables. A fundamental result is Cramér’s theorem, which states that the empirical mean of a sequence of i.i.d. random variables satisfies a so called large deviations principle. Mogulskii’s theorem is concerned with the corresponding path space large deviations. To study the analogue of these theorems for a Riemannian manifold, we introduce a generalization of random walks to a manifold, called geodesic random walks. We present the analogues of Cramér’s and Mogulskii’s theorem for geodesic random walks and write down the rate function for these large deviations principles.