02715nam 22004575 450 991030010950332120200630033335.03-319-77019-510.1007/978-3-319-77019-2(CKB)4100000003359504(MiAaPQ)EBC5377509(DE-He213)978-3-319-77019-2(PPN)226697789(EXLCZ)99410000000335950420180430d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierPath Coupling and Aggregate Path Coupling /by Yevgeniy Kovchegov, Peter T. Otto1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (xi, 96 pages) illustrationsSpringerBriefs in Probability and Mathematical Statistics,2365-43333-319-77018-7 Includes bibliographical references and index.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.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.SpringerBriefs in Probability and Mathematical Statistics,2365-4333ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.519.53Kovchegov Yevgeniyauthttp://id.loc.gov/vocabulary/relators/aut767875Otto Peter Tauthttp://id.loc.gov/vocabulary/relators/autBOOK9910300109503321Path Coupling and Aggregate Path Coupling2087421UNINA