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Universality limits for entire functions

Author: Mishko Mitkovski
Journal: Proc. Amer. Math. Soc. 141 (2013), 3119-3124
MSC (2010): Primary 30D20
Published electronically: May 7, 2013
MathSciNet review: 3068965
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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

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.

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