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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hora, Akihito (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Tokyo : Springer Japan : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Colección:SpringerBriefs in Mathematical Physics, 17
Temas:
Mathematical physics.
Topological groups.
Lie groups.
Group theory.
Probabilities.
System theory.
Mathematical Physics.
Topological Groups and Lie Groups.
Group Theory and Generalizations.
Probability Theory.
Complex Systems.
Theoretical, Mathematical and Computational Physics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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