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The Limit Shape Problem for Ensembles of Young Diagrams (Paperback, 1st ed. 2016)
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The Limit Shape Problem for Ensembles of Young Diagrams (Paperback, 1st ed. 2016)
Series: SpringerBriefs in Mathematical Physics, 17
Expected to ship within 10 - 15 working days
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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.
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