Abstract
We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance $N^{-3/4+\beta}$ for some positive $\beta>0$. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.
Citation
Laszlo Erdos. Jose Ramirez. Benjamin Schlein. Horng-Tzer Yau. "Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation." Electron. J. Probab. 15 526 - 604, 2010. https://doi.org/10.1214/EJP.v15-768
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