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Universality Under Szegő’s Condition

Published online by Cambridge University Press:  20 November 2018

Vilmos Totik
Vilmos Totik*
Affiliation:
MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged, Szeged, Aradi v. tere 1, 6720, Hungary and Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave, CMCh z, Tampa, FL 33620-5700, USA e-mail: totik@mail.usf.edu
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Abstract

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This paper presents a theoremon universality on orthogonal polynomials/randommatrices 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 that are Lebesgue-points for both the weight function $w$ and $\log \,w$ .

Keywords

42C0560B2030C8531A15universalityrandom matricesChristoòel functionsasymptoticspotential theory
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016 , pp. 211 - 224
Copyright
Copyright © Canadian Mathematical Society 2016

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