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General β‐Jacobi Corners Process and the Gaussian Free Field
Author(s) -
Borodin Alexei,
Gorin Vadim
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21546
Subject(s) - mathematics , gaussian free field , connection (principal bundle) , parallels , gaussian , hypergeometric function , field (mathematics) , pure mathematics , limit (mathematics) , random matrix , mathematical analysis , geometry , quantum mechanics , physics , mechanical engineering , eigenvalues and eigenvectors , engineering
We prove that the two‐dimensional Gaussian free field describes the asymptotics of global fluctuations of a multilevel extension of the general β‐Jacobi random matrix ensembles. Our approach is based on the connection of the Jacobi ensembles to a degeneration of the Macdonald processes that parallels the degeneration of the Macdonald polynomials to the Heckman‐Opdam hypergeometric functions (of type A). We also discuss the β → ∞ limit. © 2015 Wiley Periodicals, Inc.
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