Gap universality of generalized Wigner and β ensembles Journal Article


Author(s): Erdős, László; Yau, Horng-Tzer
Article Title: Gap universality of generalized Wigner and β ensembles
Affiliation IST Austria
Abstract: We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β ≥ 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any C4(ℝ) potential.
Keywords: Gap distribution; Log-gas; Wigner-Dyson-Gaudin-Mehta universality; β-ensembles
Journal Title: Journal of the European Mathematical Society
Volume: 17
Issue 8
ISSN: 1435-9863
Publisher: European Mathematical Society  
Date Published: 2015-08-01
Start Page: 1927
End Page: 2036
URL:
DOI: 10.4171/JEMS/548
Open access: yes (repository)
IST Austria Authors
  1. László Erdős
    110 Erdős
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