Band 17
The Limit Shape Problem for Ensembles of Young Diagrams
Aus der Reihe
SpringerBriefs in Mathematical Physics
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- Taschenbuch ausgewählt
- eBook
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Sprache:Englisch
Fr. 73.90
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
17.11.2016
Abbildungen
IX, 9 illus., schwarz-weiss Illustrationen
Verlag
Springer TokyoSeitenzahl
73
Maße (L/B/H)
24.1/15.9/0.9 cm
Gewicht
154 g
Auflage
1st ed. 2016
Sprache
Englisch
ISBN
978-4-431-56485-0
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.
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