INTRODUCTION TO HYDRODYNAMIC LIMITS AND FLUCTUATIONS

Hydrodynamic limits allow to derive some PDE as scaling limits of random systems with many degrees of freedom. The aim of the lectures is to introduce the main probabilistic ideas of hydrodynamic limits. The course is organized in such a way that no special knowledge of probability is required.

The main topics will be the following:
1) Limit theorems in probability theory. Fluctuations, large deviations.
2) Random systems with many components, interacting particle systems.
3) Scalings, hydrodynamic limits.
4) Entropy, fluctuations, Onsager-Machlup theory.