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# Universality Under Szegő's Condition

Published:2015-07-14
Printed: Mar 2016
• Vilmos Totik,
Department of Mathematics and Statistics , University of South Florida , 4202 E. Fowler Ave, CMC342 , Tampa, FL 33620-5700, USA
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## Abstract

This paper presents a theorem on universality on orthogonal polynomials/random matrices under a weak local condition on the weight function $w$. With a new inequality for polynomials and with the use of fast decreasing polynomials, it is shown that an approach of D. S. Lubinsky is applicable. The proof works at all points which are Lebesgue-points both for the weight function $w$ and for $\log w$.
 Keywords: universality, random matrices, Christoffel functions, asymptotics, potential theory
 MSC Classifications: 42C05 - Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45] 60B20 - Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 30C85 - Capacity and harmonic measure in the complex plane [See also 31A15] 31A15 - Potentials and capacity, harmonic measure, extremal length [See also 30C85]

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