General β-Jacobi Corners Process and the Gaussian Free Field
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 parallel...
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| Format: | Article |
| Language: | en_US |
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Wiley Blackwell
2017
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| Online Access: | http://hdl.handle.net/1721.1/110685 https://orcid.org/0000-0002-2913-5238 https://orcid.org/0000-0002-9828-5862 |
| _version_ | 1811069229615546368 |
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| author | Borodin, Alexei Gorin, Vadim |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Gorin, Vadim |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:07:46Z |
| format | Article |
| id | mit-1721.1/110685 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:07:46Z |
| publishDate | 2017 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/1106852022-09-23T11:07:59Z General β-Jacobi Corners Process and the Gaussian Free Field Borodin, Alexei Gorin, Vadim Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Gorin, Vadim 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. 2017-07-12T17:45:59Z 2017-07-12T17:45:59Z 2015-08 2013-06 Article http://purl.org/eprint/type/JournalArticle 0010-3640 1097-0312 http://hdl.handle.net/1721.1/110685 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 https://orcid.org/0000-0002-2913-5238 https://orcid.org/0000-0002-9828-5862 en_US http://dx.doi.org/10.1002/cpa.21546 Communications on Pure and Applied Mathematics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley Blackwell arXiv |
| spellingShingle | Borodin, Alexei Gorin, Vadim General β-Jacobi Corners Process and the Gaussian Free Field |
| title | General β-Jacobi Corners Process and the Gaussian Free Field |
| title_full | General β-Jacobi Corners Process and the Gaussian Free Field |
| title_fullStr | General β-Jacobi Corners Process and the Gaussian Free Field |
| title_full_unstemmed | General β-Jacobi Corners Process and the Gaussian Free Field |
| title_short | General β-Jacobi Corners Process and the Gaussian Free Field |
| title_sort | general β jacobi corners process and the gaussian free field |
| url | http://hdl.handle.net/1721.1/110685 https://orcid.org/0000-0002-2913-5238 https://orcid.org/0000-0002-9828-5862 |
| work_keys_str_mv | AT borodinalexei generalbjacobicornersprocessandthegaussianfreefield AT gorinvadim generalbjacobicornersprocessandthegaussianfreefield |