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The Limit Shape Problem for Ensembles of Young Diagrams

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 fo...

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Bibliographic Details
Main Author: Hora, Akihito
Format: eBook
Language:English
Published: Tokyo Springer Japan 2016, 2016
Edition:1st ed. 2016
Series:SpringerBriefs in Mathematical Physics
Subjects:
Group Theory
Statistical Physics And Dynamical Systems
Topological Groups, Lie Groups
Lie Groups
Statistical Physics
Topological Groups
Mathematical Physics
Complex Systems
Group Theory And Generalizations
Probability Theory And Stochastic Processes
Dynamical Systems
Probabilities
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 1. Introduction
  • 2. Prerequisite materials
  • 2.1 representations of the symmetric group
  • 2.2 free probability
  • 2.3 ensembles of Young diagrams
  • 3. Analysis of the Kerov—Olshanski algebra
  • 3.1 polynomial functions of Young diagrams
  • 3.2 Kerov polynomials
  • 4. Static model
  • 4.1 Plancherel ensemble
  • 4.2 Thoma and other ensembles
  • 5. Dynamic model
  • 5.1 hydrodynamic limit for the Plancherel ensemble

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