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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dc.contributor.author	Lubinsky, D.S.
dc.date.accessioned	2019-02-16T09:12:52Z
dc.date.available	2019-02-16T09:12:52Z
dc.date.issued	2016
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 15B52; 60B20; 60F99; 42C05; 33C50
dc.identifier.other	DOI:10.3842/SIGMA.2016.078
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147843
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA