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962750700 |
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20240329122006.0 |
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|a Hora, Akihito,
|e author.
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| 245 |
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|a The limit shape problem for ensembles of young diagrams /
|c Akihito Hora.
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| 264 |
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|a Tokyo, Japan :
|b Springer,
|c 2016.
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| 300 |
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|a 1 online resource (ix, 73 pages) :
|b illustrations.
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|a text
|b txt
|2 rdacontent.
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|a computer
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|a online resource
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|b PDF.
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1 |
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|a SpringerBriefs in mathematical physics,
|x 2197-1757 ;
|v volume 17.
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| 504 |
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|a Includes bibliographical references and index.
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|a Online resource; title from PDF title page (SpringerLink, viewed November 22, 2016).
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|a Preface; Contents; 1 Preliminaries; 1.1 Representations of Symmetric Groups; 1.2 Young Graph; 1.3 Free Probability; 2 Analysis of the Kerov -- Olshanski Algebra; 2.1 Coordinates of a Young Diagram; 2.2 Transition Measure I; 2.3 The Kerov -- Olshanski Algebra; 3 Continuous Diagram; 3.1 Continuous Diagram I; 3.2 Transition Measure II; 3.3 Continuous Diagram II; 4 Static Model; 4.1 Balanced Young Diagrams; 4.2 Convergence to the Limit Shape; 4.3 Continuous Hook and the Limit Shape; 4.4 Approximate Factorization Property; 5 Dynamic Model; 5.1 Restriction-Induction Chain; 5.2 Diffusive Limit.
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|a 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.
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|a Limit cycles.
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|a Cycles limites.
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|a MATHEMATICS
|x Calculus.
|2 bisacsh.
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| 650 |
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7 |
|a MATHEMATICS
|x Mathematical Analysis.
|2 bisacsh.
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| 650 |
|
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|a Matemáticas
|x Análisis matemático.
|2 embne.
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| 650 |
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|a Ciclos límite.
|2 embucm.
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| 650 |
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|a Limit cycles.
|2 fast.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 776 |
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|i Printed edition:
|z 9784431564850.
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| 830 |
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|a SpringerBriefs in mathematical physics ;
|v v. 17.
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