Universality limits for entire functions

Mitkovski, Mishko

doi:10.1090/S0002-9939-2013-11585-6

Universality limits for entire functions
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by Mishko Mitkovski PDF

Proc. Amer. Math. Soc. 141 (2013), 3119-3124 Request permission

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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