Path Coupling and Aggregate Path Coupling

1. Auflage 2018
ISBN: 978-3-319-77018-5
Verlag: Springer

Buch, Englisch, 96 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 180 g

Reihe: SpringerBriefs in Probability and Mathematical Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kovchegov, Yevgeniy

Otto, Peter T.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.