21.10.2026

Juliane Krautz Title:  Large Deviations and Gradient Flows

Abstract:  Large deviations theory quantifies the probabilities of rare events and describes how systems behave when such events occur. I will motivate the theory and give an overview of two of its core ideas in a simple discrete setting. First, we discuss Cramér's theorem for sums of i.i.d. random variables, then pass to Sanov's theorem for empirical measures. In the second part, we turn to the role of large deviations in the context of gradient flows. To this end, we compare the large deviations rate function with the minimizing movement functional and discuss how entropy arises as the driving functional of the dynamics.