Electronic Journal of Probability

Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation

Laszlo Erdos, Jose Ramirez, Benjamin Schlein, and Horng-Tzer Yau

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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.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 18, 526-604.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819803

Digital Object Identifier
doi:10.1214/EJP.v15-768

Mathematical Reviews number (MathSciNet)
MR2639734

Zentralblatt MATH identifier
1225.15034

Subjects
Primary: 15A52
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Wigner random matrix Dyson sine kernel

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Erdos, Laszlo; Ramirez, Jose; Schlein, Benjamin; Yau, Horng-Tzer. Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation. Electron. J. Probab. 15 (2010), paper no. 18, 526--604. doi:10.1214/EJP.v15-768. https://projecteuclid.org/euclid.ejp/1464819803


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