# Stochastic origins of gradient flows:a general connection

### (Technische Universiteit Eindhoven)

**Event:** ERC Workshop on Optimal Transportation and Applications

**Date:** Oct 27, 2014,
**time:** 09:00

**Abstract.**

Although it has been known for some time that certain gradient-ﬂow structures are related to the large deviations of a stochastic process, until recently we only understood this at the level of examples. In this lecture I will explain a general structure that gives rise to the following property: for every sequence of reversible stochastic processes with a large-deviations principle, the limiting equation is a generalized gradient ﬂow that maps one-to-one to the large-deviations rate function. Therefore the large class of reversible stochastic processes generates a correspondingly large class of generalized gradient ﬂows. This is joint work with Michiel Renger and Alexander Mielke.