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.
