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arXiv · 1010.0898

CLT for spectra of submatrices of Wigner random matrices

Alexei Borodin
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Abstract

We prove a CLT for spectra of submatrices of real symmetric and Hermitian Wigner matrices. We show that if in the standard normalization the fourth moment of the off-digonal entries is GOE/GUE-like then the limiting Gaussian process can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields.

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Alexei Borodin. 2010-10-05. CLT for spectra of submatrices of Wigner random matrices. https://arxiv.org/abs/1010.0898

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