CLT for spectra of submatrices of Wigner random matrices

Details CLT for spectra of submatrices of Wigner random matrices CLT for spectra of submatrices of Wigner random matrices

2010-10-05

arxiv.org/abs/1010.0898v1

Mathematics

Probability

Scientific paper

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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