Universality limits for entire functions

Author:
Mishko Mitkovski

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3119-3124

MSC (2010):
Primary 30D20

DOI:
https://doi.org/10.1090/S0002-9939-2013-11585-6

Published electronically:
May 7, 2013

MathSciNet review:
3068965

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Abstract | References | Similar Articles | Additional Information

Abstract: Various statements on the distribution of eigenvalues of random matrices are obtained by considering the limiting behavior of the reproducing kernels of a certain naturally associated sequence of orthogonal polynomials. We establish a universal limiting behavior of this type in the case when the underlying measure does not have finite moments. In this case the orthogonal polynomials are replaced by a nested family of de Branges spaces of entire functions.

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Additional Information

**Mishko Mitkovski**

Affiliation:
School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160

Address at time of publication:
Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634

Email:
mishko@math.gatech.edu, mmitkov@clemson.edu

DOI:
https://doi.org/10.1090/S0002-9939-2013-11585-6

Keywords:
Universality limits,
entire functions,
reproducing kernels

Received by editor(s):
November 14, 2011

Published electronically:
May 7, 2013

Additional Notes:
The author was supported in part by NSF grants #DMS-1001098 and #DMS-1101251.

Communicated by:
Richard Rochberg

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.