Path Coupling and Aggregate Path Coupling (Springerbriefs in Probability and Mathematical Statistics) （2018）

Kovchegov, Yevgeniy/ Otto, Peter T.

Springer International Publishing AG（2018/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 96 p.
• 商品コード 9783319770185

Full Description

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.

Contents

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.