PDE methods for statistical physics

Orateur: ROUSSEL Julien
Localisation: ENPC, France
Type: Séminaire des doctorants
Site: UGE
Salle: B211, bâtiment Coriolis
Date de début: 09/11/2016 - 16:00
Date de fin: 09/11/2016 - 16:00

The Langevin Dynamics and the Overdamped Langevin dynamics are two widely used stochastic models which describe systems at a microscopic level. In a first part I introduce these dynamics and how macroscopic properties are deduced from statistics on the trajectories. Then I define the generator of such a stochastic differential equation (SDE), which is a differential operator, and show how its properties can be linked to the speed of convergence of the empirical averages. Finally I focus on the Langevin dynamics and explain what is the hypocoercivity. I may have time to speak about Galerkin methods for hypocoercive problems.