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2012 A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
László Erdős, Horng-Tzer Yau
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Electron. J. Probab. 17: 1-5 (2012). DOI: 10.1214/EJP.v17-1779

Abstract

Recently we proved that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices. Tao and Vu gave a proof that for the special case of Hermitian Wigner matrices the convergence can be strengthened to vague convergence at any fixed energy in the bulk. In this article we comment on this result in the context of the universality conjectures of Mehta. We show that this theorem is an immediate corollary of our earlier results. Indeed, a more general form of this theorem also follows directly from our previous work.

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László Erdős. Horng-Tzer Yau. "A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices." Electron. J. Probab. 17 1 - 5, 2012. https://doi.org/10.1214/EJP.v17-1779

Information

Accepted: 10 April 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1245.15038
MathSciNet: MR2915664
Digital Object Identifier: 10.1214/EJP.v17-1779

Subjects:
Primary: 15A52
Secondary: 82B44

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Vol.17 • 2012
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