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.