General β‐Jacobi Corners Process and the Gaussian Free Field. Issue 10 (10th October 2014)

• Record Type: Journal Article
• Authors: Borodin, Alexei; Gorin, Vadim
• Is Part Of: Communications on pure and applied mathematics. Volume 68:Issue 10(2015:Oct.)
• Page Start: 1774
• Page End: 1844
• Publication Date: 2014-10-10
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21546
• Languages: English
• ISSNs: 0010-3640

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>We prove that the two‐dimensional Gaussian free field describes the asymptotics of global fluctuations of a multilevel extension of the general β‐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 the Heckman‐Opdam hypergeometric functions (of type A). We also discuss the β → ∞ limit. © 2015 Wiley Periodicals, Inc.</p> </abstract>