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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
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.
Received: April 5, 2016; in final form August 5, 2016; Published online August 10, 2016
Citation:
Doron S. Lubinsky, “An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles”, SIGMA, 12 (2016), 078, 36 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1160 https://www.mathnet.ru/eng/sigma/v12/p78
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Abstract page: | 155 | Full-text PDF : | 40 | References: | 46 |
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