LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	530.15
Title	The Limit Shape Problem for Ensembles of Young Diagrams ([EBook]) / by Akihito Hora.
Author	Hora, Akihito
Other name(s)	SpringerLink (Online service)
Publication	Tokyo : : Springer Japan : : Imprint: Springer, , 2016.
Physical Details	IX, 73 p. 9 illus. : online resource.
Series	SpringerBriefs in Mathematical Physics 2197-1757 ; ; 17
ISBN	9784431564874
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-4-431-56487-4
Links to Related Works	Subject References: Complex Systems . Group theory . Group Theory and Generalizations . Lie groups . Mathematical Physics . Mathematics . Probabilities . Probability theory and stochastic processes . Statistical Physics and Dynamical Systems . System theory . Topological groups . Topological groups, Lie groups . Authors: Hora, Akihito . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematical Physics . Classification: 530.15 .

Catalogue Display

The Limit Shape Problem for Ensembles of Young Diagrams

Reviews