The Limit Shape Problem for Ensembles of Young Diagrams

  • Akihito Hora

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 17)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Akihito Hora
    Pages 1-13
  3. Akihito Hora
    Pages 31-41
  4. Akihito Hora
    Pages 43-60
  5. Akihito Hora
    Pages 61-68
  6. Back Matter
    Pages 69-73

About this book

Introduction

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.

Keywords

Limit shape Ensemble of Young diagrams Symmetric group Free probability Diffusive limit

Authors and affiliations

  • Akihito Hora
    • 1
  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-4-431-56487-4
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Tokyo
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-4-431-56485-0
  • Online ISBN 978-4-431-56487-4
  • Series Print ISSN 2197-1757
  • Series Online ISSN 2197-1765
  • About this book