Path Coupling and Aggregate Path Coupling [Paperback]

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.

Preface.- 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.
Provides a comprehensive background on coupling and path coupling

Can be used as a standalone research monograph

Considered to be the first comprehensive book on the topic
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