Gaussian asymptotics of discrete β β -ensembles
© 2016, IHES and Springer-Verlag Berlin Heidelberg. We introduce and study stochastic N-particle ensembles which are discretizations for general-β log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, (z, w) -measures, etc. We prove that under te...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Nature
2021
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| Online Access: | https://hdl.handle.net/1721.1/133899 |
| _version_ | 1826191669627715584 |
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| author | Borodin, Alexei Gorin, Vadim Guionnet, Alice |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Gorin, Vadim Guionnet, Alice |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | © 2016, IHES and Springer-Verlag Berlin Heidelberg. We introduce and study stochastic N-particle ensembles which are discretizations for general-β log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, (z, w) -measures, etc. We prove that under technical assumptions on general analytic potential, the global fluctuations for such ensembles are asymptotically Gaussian as N→ ∞. The covariance is universal and coincides with its counterpart in random matrix theory. Our main tool is an appropriate discrete version of the Schwinger-Dyson (or loop) equations, which originates in the work of Nekrasov and his collaborators. |
| first_indexed | 2024-09-23T08:59:32Z |
| format | Article |
| id | mit-1721.1/133899 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:59:32Z |
| publishDate | 2021 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | mit-1721.1/1338992023-12-22T18:59:28Z Gaussian asymptotics of discrete β β -ensembles Borodin, Alexei Gorin, Vadim Guionnet, Alice Massachusetts Institute of Technology. Department of Mathematics © 2016, IHES and Springer-Verlag Berlin Heidelberg. We introduce and study stochastic N-particle ensembles which are discretizations for general-β log-gases of random matrix theory. The examples include random tilings, families of non-intersecting paths, (z, w) -measures, etc. We prove that under technical assumptions on general analytic potential, the global fluctuations for such ensembles are asymptotically Gaussian as N→ ∞. The covariance is universal and coincides with its counterpart in random matrix theory. Our main tool is an appropriate discrete version of the Schwinger-Dyson (or loop) equations, which originates in the work of Nekrasov and his collaborators. 2021-10-27T19:57:08Z 2021-10-27T19:57:08Z 2017 2021-04-28T16:58:31Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133899 en 10.1007/S10240-016-0085-5 Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Nature arXiv |
| spellingShingle | Borodin, Alexei Gorin, Vadim Guionnet, Alice Gaussian asymptotics of discrete β β -ensembles |
| title | Gaussian asymptotics of discrete β β -ensembles |
| title_full | Gaussian asymptotics of discrete β β -ensembles |
| title_fullStr | Gaussian asymptotics of discrete β β -ensembles |
| title_full_unstemmed | Gaussian asymptotics of discrete β β -ensembles |
| title_short | Gaussian asymptotics of discrete β β -ensembles |
| title_sort | gaussian asymptotics of discrete β β ensembles |
| url | https://hdl.handle.net/1721.1/133899 |
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