Kinetically constrained models
Ivailo Hartarsky, Cristina Toninelli
TL;DR
Kinetically constrained models (KCM) offer a probabilistic framework to understand glassy and jamming dynamics driven by local update constraints. The book surveys core results on relaxation, spectral gaps, and mixing times, employing tools such as bootstrap percolation, renormalization (Matryoshka-doll) techniques, and analysis on diverse graph structures, including trees and lattices. It also explores extensions with inhomogeneous constraints, interactions, and plaquette-based static Hamiltonians, as well as conservative dynamics and non-equilibrium regimes, highlighting universality in low dimensions and open problems in higher dimensions. The work aims to bridge mathematics and physics by clarifying methods, providing self-contained expositions, and outlining directions for future research in constrained dynamical systems and glassy phenomenology.
Abstract
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.