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SpringerBriefs in Mathematical Physics

The Limit Shape Problem for Ensembles of Young Diagrams

Authors: Hora, Akihito

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  • Demonstrates that the interplay of group representations and probability theory seems to be one of the international trends in mathematics
  • Provides connections for readers with other branches and hints for new research as Young diagrams appear in various aspects of mathematics and physics
  • Is written in a mathematically rigorous way using the prerequisite materials and is accessible to students and non-experts
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  • ISBN 978-4-431-56487-4
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About this book

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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $54.99
price for Mexico
  • ISBN 978-4-431-56487-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
The Limit Shape Problem for Ensembles of Young Diagrams
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
17
Copyright
2016
Publisher
Springer Japan
Copyright Holder
The Author(s)
eBook ISBN
978-4-431-56487-4
DOI
10.1007/978-4-431-56487-4
Softcover ISBN
978-4-431-56485-0
Series ISSN
2197-1757
Edition Number
1
Number of Pages
IX, 73
Number of Illustrations
9 b/w illustrations
Topics