Large deviations

Basics notions of what are large deviations, motivations from finance, insurance, statistical physics, and probability theory.

Large deviations for sums of iid random variables, Cramer's theorem.

Large deviations for empirical measure, Sanov's theorem.

Large deviations for interacting processes: endpoint of a self-avoiding-walk.

General principles in large deviation theory, large deviation principles in metric spaces, general versions of Cramer's and Sanov's theorems, Gartner-Ellis theorem.

Large deviations and phase transitions in statistical physics models.