General β-Jacobi Corners Process and the Gaussian Free Field

General β-Jacobi Corners Process and the Gaussian Free Field

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 parallel...

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Bibliographic Details
Main Authors: Borodin, Alexei (Contributor), Gorin, Vadim (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Wiley Blackwell, 2017-07-12T17:45:59Z.
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Summary: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.

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