Kovchegov Y., Otto P.T. Path Coupling and Aggregate Path Coupling

Springer International Publishing AG, 2018. — 104 p. — (SpringerBriefs in Probability and Mathematical Statistics). — ISBN: 3319770187.This book describes and characterizes an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggregate path coupling. In conjunction with large deviations estimates, the aggregate path coupling method is used to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The book shows how the parameter regions for rapid mixing for several classes of statistical mechanical models are derived using the aggregate path coupling method.Coupling, Path Coupling, and Mixing Times
Statistical Mechanical Models and Glauber Dynamics
Large Deviations and Equilibrium Macrostate Phase Transitions
Path Coupling for Curie-Weiss Model
Aggregate Path Coupling: One-Dimensional Theory
Aggregate Path Coupling: Higher Dimensional Theory
Aggregate Path Coupling: Beyond Kn