Benoit Dagallier Imperial College

The Polchinski dynamics: an introduction

Abstract:

I will introduce the Polchinski dynamics (or flow), 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 very different contexts (Markov chain mixing, optimal transport, functional inequalities...) Here I will motivate its construction from a physics point of view and mention a few applications. In particular, I will explain how the Polchinski flow can be used to generalise Bakry and Emery's Γ₂ calculus to obtain functional inequalities (e.g. Poincaré, log-Sobolev) in physics models which are typically high-dimensional and non-convex. The talk is based on a review paper with Roland Bauerschmidt and Thierry Bodineau, accessible here