General beta Jacobi corners process and the Gaussian Free Field
Abstract
We prove that the twodimensional 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 HeckmanOpdam hypergeometric functions (of type A). We also discuss the beta goes to infinity limit.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 arXiv:
 arXiv:1305.3627
 Bibcode:
 2013arXiv1305.3627B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 59 pages, 4 figures. v4: corrected inaccuracy in the definition of the pullback of the GFF