Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation

L. Erdös, J. Ramírez, B. Schlein, H. Yau, Electronic Journal of Probability 15 (2010) 526–603.

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Abstract
We consider N × 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+β for some positive β > 0. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.
Publishing Year
Date Published
2010-01-01
Journal Title
Electronic Journal of Probability
Volume
15
Issue
18
Page
526 - 603
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Erdös L, Ramírez J, Schlein B, Yau H. Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation. Electronic Journal of Probability. 2010;15(18):526-603. doi:10.1214/EJP.v15-768
Erdös, L., Ramírez, J., Schlein, B., & Yau, H. (2010). Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation. Electronic Journal of Probability, 15(18), 526–603. https://doi.org/10.1214/EJP.v15-768
Erdös, László, José Ramírez, Benjamin Schlein, and Horng Yau. “Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation.” Electronic Journal of Probability 15, no. 18 (2010): 526–603. https://doi.org/10.1214/EJP.v15-768.
L. Erdös, J. Ramírez, B. Schlein, and H. Yau, “Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation,” Electronic Journal of Probability, vol. 15, no. 18, pp. 526–603, 2010.
Erdös L, Ramírez J, Schlein B, Yau H. 2010. Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation. Electronic Journal of Probability. 15(18), 526–603.
Erdös, László, et al. “Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation.” Electronic Journal of Probability, vol. 15, no. 18, Institute of Mathematical Statistics, 2010, pp. 526–603, doi:10.1214/EJP.v15-768.

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