General beta Jacobi corners process and the Gaussian Free Field
Probability
2017-04-14 v4 Mathematical Physics
math.MP
Representation Theory
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.
Keywords
Cite
@article{arxiv.1305.3627,
title = {General beta Jacobi corners process and the Gaussian Free Field},
author = {Alexei Borodin and Vadim Gorin},
journal= {arXiv preprint arXiv:1305.3627},
year = {2017}
}
Comments
59 pages, 4 figures. v4: corrected inaccuracy in the definition of the pullback of the GFF