English

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