TY - BOOK ID - 14228400 TI - The limit shape problem for ensembles of Young diagrams PY - 2016 SN - 4431564853 443156487X PB - Tokyo : Springer Japan : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Group theory. KW - Topological groups. KW - Lie groups. KW - System theory. KW - Probabilities. KW - Mathematical physics. KW - Mathematical Physics. KW - Topological Groups, Lie Groups. KW - Group Theory and Generalizations. KW - Probability Theory and Stochastic Processes. KW - Complex Systems. KW - Statistical Physics and Dynamical Systems. KW - Limit cycles. KW - Limit cycles KW - Cycles, Limit KW - Differential equations KW - Limit cycles of differential equations KW - Physical mathematics KW - Physics KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Systems, Theory of KW - Systems science KW - Science KW - Groups, Lie KW - Lie algebras KW - Symmetric spaces KW - Topological groups KW - Groups, Topological KW - Continuous groups KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Math KW - Philosophy KW - Differentiable dynamical systems KW - Topological Groups. KW - Distribution (Probability theory. KW - Statistical physics. KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Statistical methods KW - Dynamical systems. KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14228400 AB - 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. ER -