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October 2009 Universality and fine zero spacing on general sets
Vilmos Totik
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Ark. Mat. 47(2): 361-391 (October 2009). DOI: 10.1007/s11512-008-0071-3

Abstract

A recent approach of D. S. Lubinsky yields universality in random matrix theory and fine zero spacing of orthogonal polynomials under very mild hypothesis on the weight function, provided the support of the generating measure μ is [-1,1]. This paper provides a method with which analogous results can be proven on general compact subsets of R. Both universality and fine zero spacing involves the equilibrium measure of the support of μ. The method is based on taking polynomial inverse images, by which results can be transferred from [-1,1] to a system of intervals, and then to general sets.

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Vilmos Totik. "Universality and fine zero spacing on general sets." Ark. Mat. 47 (2) 361 - 391, October 2009. https://doi.org/10.1007/s11512-008-0071-3

Information

Received: 6 August 2007; Published: October 2009
First available in Project Euclid: 31 January 2017

zbMATH: 1180.42017
MathSciNet: MR2529707
Digital Object Identifier: 10.1007/s11512-008-0071-3

Rights: 2008 © Institut Mittag-Leffler

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Vol.47 • No. 2 • October 2009
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