The Limit Shape Problem for Ensembles of Young Diagrams / SpringerBriefs in Mathematical Physics Bd.17 (PDF)
(Sprache: Englisch)
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...
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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.
Bibliographische Angaben
- Autor: Akihito Hora
- 2016, 1st ed. 2016, 73 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 443156487X
- ISBN-13: 9784431564874
- Erscheinungsdatum: 09.11.2016
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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- Dateiformat: PDF
- Größe: 1.47 MB
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Sprache:
Englisch
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