Statistical Mechanics and Stochastic PDEs

This volume collects the lecture notes of the CIME Summer School “Statistical Mechanics and Stochastic PDEs”, held in Cetraro, Italy, on 11–15 September 2023. It offers an up-to-date account of recent developments at the interface between statistical mechanics and stochastic PDEs, areas that have witnessed fundamental breakthroughs and gained wide recognition in recent years. The book explores the interplay between discrete models of statistical mechanics and continuum SPDEs, focusing in particular on questions of universality, the crucial role played by dimension, and the use of ideas from renormalization group theory to study both settings. Topics covered include the large-scale behavior of critical and supercritical stochastic PDEs, by G. Cannizzaro and F. L. Toninelli; an introduction to FK percolation, by I. Manolescu; a constructive approach to stochastic quantization, by M. Gubinelli; and the critical two-dimensional stochastic heat flow, by F. Caravenna, R. Sun and N. Zygouras. The book is aimed at graduate students and researchers interested in probability theory, stochastic analysis, mathematical physics, and the interplay between these fields.