## Probability Seminar

I will discuss a general framework to obtain large scale information in statistical mechanics and field theory models. The basic idea is to obtain information from the model by constructing a dynamics that samples from it and analysing the long-time behaviour of the dynamics. The Langevin dynamics is a typical example of such a dynamics. In this talk I will introduce another, the Polchinski dynamics, based on renormalisation group ideas. The dynamics is parametrised by a parameter representing scale and has a number of interesting properties that make it well suited to study large-dimensional models. It is perhaps better known under the name stochastic localisation. I will mention a number of recent applications of this dynamics, in particular to prove functional inequalities via a generalisation of Bakry and Emery's convexity-based argument. The talk is based on joint work with Roland Bauerschmidt and Thierry Bodineau and the recent review paper https://arxiv.org/abs/2307.07619 .