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arXiv · 1305.3627

General beta Jacobi corners process and the Gaussian Free Field

Alexei Borodin·Vadim Gorin
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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 beta 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 to the Heckman-Opdam hypergeometric functions (of type A). We also discuss the beta goes to infinity limit.

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Alexei Borodin, Vadim Gorin. 2017-04-13. General beta Jacobi corners process and the Gaussian Free Field. https://arxiv.org/abs/1305.3627

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