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Universality and fine zero spacing on general sets

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Arkiv för Matematik

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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Authors and Affiliations

  1. Bolyai Institute, Analysis Research Group of the Hungarian Academy of Sciences, University of Szeged, Aradi v. tere 1, Szeged, HU-6720, Hungary

    Vilmos Totik

  2. Department of Mathematics, University of South Florida, 4202 E. Fowler Ave, PHY 114, Tampa, FL, 33620-5700, USA

    Vilmos Totik

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  1. Vilmos Totik
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Correspondence to Vilmos Totik.

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

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  • DOI: https://doi.org/10.1007/s11512-008-0071-3

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