A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices

L. Erdös, H. Yau, Electronic Journal of Probability 17 (2012).

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Abstract
Recently we proved [3, 4, 6, 7, 9, 10, 11] 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 [15] 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 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 work [2].
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Date Published
2012-04-10
Journal Title
Electronic Journal of Probability
Volume
17
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Erdös L, Yau H. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 2012;17. doi:10.1214/EJP.v17-1779
Erdös, L., & Yau, H. (2012). A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability, 17. https://doi.org/10.1214/EJP.v17-1779
Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability 17 (2012). https://doi.org/10.1214/EJP.v17-1779.
L. Erdös and H. Yau, “A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices,” Electronic Journal of Probability, vol. 17, 2012.
Erdös L, Yau H. 2012. A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices. Electronic Journal of Probability. 17.
Erdös, László, and Horng Yau. “A Comment on the Wigner-Dyson-Mehta Bulk Universality Conjecture for Wigner Matrices.” Electronic Journal of Probability, vol. 17, Institute of Mathematical Statistics, 2012, doi:10.1214/EJP.v17-1779.

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