The Limit Shape Problem for Ensembles of Young Diagrams

• Κύριος συγγραφέας: Hora, Akihito (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Tokyo : Springer Japan : Imprint: Springer, 2016.
• Σειρά: SpringerBriefs in Mathematical Physics, 17
• Θέματα: Mathematics.; Group theory.; Topological groups.; Lie groups.; System theory.; Probabilities.; Mathematical physics.; Mathematical Physics.; Topological Groups, Lie Groups.; Group Theory and Generalizations.; Probability Theory and Stochastic Processes.; Complex Systems.; Statistical Physics and Dynamical Systems.

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...

Πίνακας περιεχομένων:

• 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.