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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 078, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.078
(Mi sigma1160)
 

This article is cited in 13 scientific papers (total in 13 papers)

An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles

Doron S. Lubinsky

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160 USA
References:
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 $\beta$ ensembles for $\beta \neq 2$, nor general Hermitian matrices with independent entries, let alone more general settings. We include some open problems.
Keywords: orthogonal polynomials; random matrices; unitary ensembles; correlation functions; Christoffel functions.
Funding agency Grant number
National Science Foundation DMS1362208
Research supported by NSF grant DMS1362208.
Received: April 5, 2016; in final form August 5, 2016; Published online August 10, 2016
Bibliographic databases:
Document Type: Article
Language: English
Citation: Doron S. Lubinsky, “An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles”, SIGMA, 12 (2016), 078, 36 pp.
Citation in format AMSBIB
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\paper An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles
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\vol 12
\papernumber 078
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  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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