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2010 Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation
Laszlo Erdos, Jose Ramirez, Benjamin Schlein, Horng-Tzer Yau
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Electron. J. Probab. 15: 526-604 (2010). DOI: 10.1214/EJP.v15-768

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.

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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

Information

Accepted: 1 May 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1225.15034
MathSciNet: MR2639734
Digital Object Identifier: 10.1214/EJP.v15-768

Subjects:
Primary: 15A52
Secondary: 82B44

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