Z-measures on partitions and their scaling limits

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dc.creatorBorodin, Alexei
dc.creatorOlshanski, Grigori
dc.date2002-10-28
dc.date.accessioned2026-07-07T07:37:00Z
dc.date.available2026-07-07T07:37:00Z
dc.descriptionWe study certain probability measures on partitions of n=1,2,..., originated in representation theory, and demonstrate their connections with random matrix theory and multivariate hypergeometric functions. Our measures depend on three parameters including an analog of the beta parameter in random matrix models. Under an appropriate limit transition as n goes to infinity, our measures converge to certain limit measures, which are of the same nature as one-dimensional log-gas with arbitrary beta>0. The first main result says that averages of products of ``characteristic polynomials'' with respect to the limit measures are given by the multivariate hypergeometric functions of type (2,0). The second main result is a computation of the limit correlation functions for the even values of beta.
dc.descriptionAMSTeX, 37 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0210048
dc.identifierhttp://arxiv.org/abs/math-ph/0210048
dc.identifierEuropean J. Combin. 26 (2005), no. 6, 795--834
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120626
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectCombinatorics
dc.subjectProbability
dc.subjectRepresentation Theory
dc.subjectExactly Solvable and Integrable Systems
dc.titleZ-measures on partitions and their scaling limits
dc.typetext

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