Gap universality of generalized Wigner and β ensembles

L. Erdös, H. Yau, Journal of the European Mathematical Society 17 (2015) 1927–2036.


Journal Article | Published | English
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Department
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.
Publishing Year
Date Published
2015-08-01
Journal Title
Journal of the European Mathematical Society
Volume
17
Issue
8
Page
1927 - 2036
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Cite this

Erdös L, Yau H. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 2015;17(8):1927-2036. doi:10.4171/JEMS/548
Erdös, L., & Yau, H. (2015). Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society, 17(8), 1927–2036. https://doi.org/10.4171/JEMS/548
Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” Journal of the European Mathematical Society 17, no. 8 (2015): 1927–2036. https://doi.org/10.4171/JEMS/548.
L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,” Journal of the European Mathematical Society, vol. 17, no. 8, pp. 1927–2036, 2015.
Erdös L, Yau H. 2015. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 17(8), 1927–2036.
Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” Journal of the European Mathematical Society, vol. 17, no. 8, European Mathematical Society, 2015, pp. 1927–2036, doi:10.4171/JEMS/548.

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