An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
We survey the current status of universality limits for m-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider underlying measures on compact intervals, and fixed and varying e...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147843 |
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| Cite this: | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles / D.S. Lubinsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 98 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862704980267368448 |
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| author | Lubinsky, D.S. |
| author_facet | Lubinsky, D.S. |
| citation_txt | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles / D.S. Lubinsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 98 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We survey the current status of universality limits for m-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider underlying measures on compact intervals, and fixed and varying exponential weights, as well as universality limits for a variety of orthogonal systems. The scope of the survey is quite narrow: we do not consider β ensembles for β≠2, nor general Hermitian matrices with independent entries, let alone more general settings. We include some open problems.
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| first_indexed | 2025-12-07T16:53:14Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147843 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:53:14Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lubinsky, D.S. 2019-02-16T09:12:52Z 2019-02-16T09:12:52Z 2016 An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles / D.S. Lubinsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 98 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 15B52; 60B20; 60F99; 42C05; 33C50 DOI:10.3842/SIGMA.2016.078 https://nasplib.isofts.kiev.ua/handle/123456789/147843 We survey the current status of universality limits for m-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider underlying measures on compact intervals, and fixed and varying exponential weights, as well as universality limits for a variety of orthogonal systems. The scope of the survey is quite narrow: we do not consider β ensembles for β≠2, nor general Hermitian matrices with independent entries, let alone more general settings. We include some open problems. This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices,
 Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy.
 The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html.
 Research supported by NSF grant DMS1362208.
 It was a privilege to attend the very high level conference celebrating Percy Deift’s 70th birthday.
 I owe Percy a great deal: it was Percy’s 60th birthday conference at the Courant Institute
 that inspired me to try apply classical methods of orthogonal polynomials to universality limits.
 Percy’s comments and perspectives, have really helped in this endeavor. Thank you, Percy –
 and thank you to CRM and the organizers of the conference.
 This survey has benefited greatly from the corrections and comments of Thomas Bothner,
 Jonathan Breuer, Tivadar Danka, Thomas Kriecherbauer, Arno Kuijlaars, Anna Maltsev, Andrei
 Mart´ınez-Finkelshtein, Barry Simon, Vili Totik, Yu-Qiu Zhao, and the anonymous referees. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles Article published earlier |
| spellingShingle | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles Lubinsky, D.S. |
| title | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles |
| title_full | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles |
| title_fullStr | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles |
| title_full_unstemmed | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles |
| title_short | An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles |
| title_sort | update on local universality limits for correlation functions generated by unitary ensembles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147843 |
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