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Universality and fine zero spacing on general sets

Vilmos Totik Bolyai Institute, Analysis Research Group of the Hungarian Academy of Sciences, University of Szeged

TBD mathscidoc:1701.333147

Arkiv for Matematik, 47, (2), 361-391, 2007.8
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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@inproceedings{vilmos2007universality,
  title={Universality and fine zero spacing on general sets},
  author={Vilmos Totik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203624848031956},
  booktitle={Arkiv for Matematik},
  volume={47},
  number={2},
  pages={361-391},
  year={2007},
}
Vilmos Totik. Universality and fine zero spacing on general sets. 2007. Vol. 47. In Arkiv for Matematik. pp.361-391. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203624848031956.
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