Kinetically Constrained Models

This book offers an in-depth review of kinetically constrained models (KCMs), a topic that lies at the crossroads of probability and statistical mechanics. KCMs have captivated physicists ever since their introduction in the 1980s. Their remarkable glassy behavior makes them an essential toy model for exploring the liquid–glass transition, a longstanding puzzle in condensed matter physics. Over the past 20 years, KCMs have also gained significant attention in mathematics. Despite belonging to the well-established domain of interacting particle systems with stochastic dynamics, the presence of dynamical constraints gives rise to novel phenomena. These include anomalously long mixing times, aging effects, singularities in the dynamical large deviation function, dynamical heterogeneities, and atypical ergodicity-breaking transitions corresponding to the emergence of a large variety of amorphous structures. Authored by two leading experts in the field, this volume offers an extensive overview of rigorous results in the field. The self-contained exposition, with emphasis on high-level ideas and common techniques, is suitable for novices, as well as seasoned researchers, with backgrounds in mathematics or physics. The text covers crucial connections to bootstrap percolation cellular automata, along with sharp thresholds, universality, out-of-equilibrium dynamics, and more. The volume features challenging open questions and a detailed bibliography to direct future research. Whether as a reference or a study guide, it is a valuable resource for those interested in KCM.