RTG Kolloquium

In this course I will introduce the Polchinski flow (or dynamics), a general framework to study asymptotic properties of statistical mechanics and field theory models, inspired by renormalisation group ideas. The Polchinski dynamics has appeared recently under different names, such as stochastic localisation, and in apparently very different contexts (Markov chain mixing, optimal transport, functional inequalities...). I will motivate the construction of this object from a physics perspective, then consider concrete statistical mechanics models where it can be used to obtain functional inequalities. The connection with (optimal) transport and stochastic localisation will be discussed, together with some open questions. The course is based on a review paper with Roland Bauerschmidt and Thierry Bodineau, accessible here: https://projecteuclid.org/journals/probability-surveys/volume-21/issue-none/Stochastic-dynamics-and-the-Polchinski-equation-An-introduction/10.1214/24-PS27.full