M2R course on stochastic processes in mathematical physics

The aim of the course is to present probabilistic approaches used to derive some of the PDEs appearing in physics. We will begin with an introduction to the stochastic processes involved (continuous-time martingales and Markov processes, Brownian motion), and then use this formalism to define and study a few random models of statistical mechanics that exhibit a deterministic macroscopic behavior driven by these evolution equations.