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The Limit Shape Problem for Ensembles of Young Diagrams

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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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Detail Information

Series Title

SpringerBriefs in Mathematical Physics

Call Number

-

Publisher

Springer Tokyo : Springer Tokyo., 2016

Collation

IX, 73

Language

English

ISBN/ISSN

978-4-431-56487-4

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

-

Edition

-

Subject(s)

Mathematical and Computational Physics

Specific Detail Info

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Statement of Responsibility

Akihito Hora

Other Information

Cataloger

Jemadi

Source

https://link.springer.com/book/10.1007/978-4-431-56487-4

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