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An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
Інший ID:
2010 Mathematics Subject Classification: 15B52; 60B20; 60F99; 42C05; 33C50
DOI:10.3842/SIGMA.2016.078
DOI:10.3842/SIGMA.2016.078
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
483
Завантажень:
230
Анотація:
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.
