General beta Jacobi corners process and the Gaussian Free Field

Understand

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.