04337nam 22007455 450 991015055100332120220407185511.04-431-56487-X10.1007/978-4-431-56487-4(CKB)3710000000943848(DE-He213)978-4-431-56487-4(MiAaPQ)EBC4740966(PPN)197139485(EXLCZ)99371000000094384820161110d2016 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierThe limit shape problem for ensembles of Young diagrams[electronic resource] /by Akihito Hora1st ed. 2016.Tokyo :Springer Japan :Imprint: Springer,2016.1 online resource (IX, 73 p. 9 illus.)SpringerBriefs in Mathematical Physics,2197-1757 ;174-431-56485-3 Includes bibliographical references and index.1. Introduction -- 2. Prerequisite materials -- 2.1 representations of the symmetric group -- 2.2 free probability -- 2.3 ensembles of Young diagrams -- 3. Analysis of the Kerov—Olshanski algebra -- 3.1 polynomial functions of Young diagrams -- 3.2 Kerov polynomials -- 4. Static model -- 4.1 Plancherel ensemble -- 4.2 Thoma and other ensembles -- 5. Dynamic model -- 5.1 hydrodynamic limit for the Plancherel ensemble.This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit. The focus is mainly on analyzing the interesting phenomenon that specific curves appear in the appropriate scaling limit for the profiles of Young diagrams. This problem is regarded as an important origin of recent vital studies on harmonic analysis of huge symmetry structures. As mathematics, an asymptotic theory of representations is developed of the symmetric groups of degree n as n goes to infinity. The framework of rigorous limit theorems (especially the law of large numbers) in probability theory is employed as well as combinatorial analysis of group characters of symmetric groups and applications of Voiculescu's free probability. The central destination here is a clear description of the asymptotic behavior of rescaled profiles of Young diagrams in the Plancherel ensemble from both static and dynamic points of view.SpringerBriefs in Mathematical Physics,2197-1757 ;17Mathematical physicsTopological groupsLie groupsGroup theoryProbabilitiesStatistical physicsDynamical systemsMathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Mathematical physics.Topological groups.Lie groups.Group theory.Probabilities.Statistical physics.Dynamical systems.Mathematical Physics.Topological Groups, Lie Groups.Group Theory and Generalizations.Probability Theory and Stochastic Processes.Complex Systems.Statistical Physics and Dynamical Systems.515.35Hora Akihitoauthttp://id.loc.gov/vocabulary/relators/aut756109MiAaPQMiAaPQMiAaPQBOOK9910150551003321Limit shape problem for ensembles of young diagrams1523681UNINA