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

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

2012-01-26

arxiv.org/abs/1201.5619v3

Mathematics

Probability

Some small typos corrected. A few explanation is added on Apr 2

Scientific paper

Recently we proved (EPRSY, ERSTVY, ESY4, ESYY, EYY, EYY2, EYYrigi) 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 \cite{TV5} 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 \cite{EKYY2}.

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