General β‐Jacobi Corners Process and the Gaussian Free Field |
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| Authors: | Alexei Borodin Vadim Gorin |
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| Affiliation: | Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA, USA |
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| 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. © 2015 Wiley Periodicals, Inc. |
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