Statistical Mechanics and Stochastic PDEs
Cetraro, Italy 2023
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Beschreibung
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.
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.
Written by leading experts in the field Presents new advances in the theory of singular stochastic PDEs and FK percolation Provides a useful survey of results in the area Additional multimedia content accessible in browser or via SN More Media App
Autor*in
Francesco Caravenna
Themen in »Statistical Mechanics and Stochastic PDEs«
Directed Polymer in Random Environment Disordered System Euclidean Quantum Field Theory Forward-Backward SDE FK Percolation KPZ Equation Burgers Equation Lindeberg Principle Phase Transition Renormalization Singular Stochastic PDE Six-Vertex Model Stochastic Heat Equation Stochastic Heat Flow Stochastic Quantisation