Publication: Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation
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Date
2010
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Institute of Mathematical Statistics
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Erdős, Laszlo, Jose Ramirez, Benjamin Schlein, and Horng-Tzer Yau. 2010. “Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation.” Electronic Journal of Probability 15 (0): 526–604. doi:10.1214/ejp.v15-768.
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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+βN−3/4+β for some positive β>0β>0. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.
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Keywords
Wigner random matrix, Dyson sine kernel
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