General β-Jacobi Corners Process and the Gaussian Free Field
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Borodin_General Jacobi.pdf
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637.72 KB
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Author(s)
Borodin, Alexei
Gorin, Vadim
Date Issued
August 2015
Journal
Communications on Pure and Applied Mathematics
Publisher
Wiley Blackwell
Citation
Borodin, Alexei, and Gorin, Vadim. “General β-Jacobi Corners Process and the Gaussian Free Field.” Communications on Pure and Applied Mathematics 68, no. 10 (October 2014): 1774–1844 © 2015 Wiley Periodicals, Inc
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/cpa.21546
