General β‐Jacobi Corners Process and the Gaussian Free Field
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Open Access
- 10 October 2014
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 68 (10) , 1774-1844
Abstract
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.Keywords
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Funding Information
- Russian Foundation for Basic Research (11-01-93105)
- National Science Foundation (DMS-1056390)
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