The Limit Shape Problem for Ensembles of Young Diagrams (Paperback, 1st ed. 2016)

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.

General

Imprint:	Springer Verlag,Japan
Country of origin:	Japan
Series:	SpringerBriefs in Mathematical Physics, 17
Release date:	November 2016
First published:	2016
Authors:	Akihito Hora
Dimensions:	235 x 155 x 4mm (L x W x T)
Format:	Paperback
Pages:	73
Edition:	1st ed. 2016
ISBN-13:	978-4-431-56485-0
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Science & Mathematics > Physics > Thermodynamics & statistical physics > Statistical physics Promotions
LSN:	4-431-56485-3
Barcode:	9784431564850

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