General beta Jacobi corners process and the Gaussian Free Field

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.

59 pages, 4 figures. v4: corrected inaccuracy in the definition of the pullback of the GFF

References in corpus (3)

• Edge Universality of Beta Ensembles
• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• Transport maps for Beta-matrix models and Universality

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