Moscow Mathematical Journal

Volume 14, Issue 1, January–March 2014 pp. 29–38.

CLT for Spectra of Submatrices of Wigner Random Matrices

Authors: Alexei Borodin
Author institution: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139, USA
IITP RAS, Bolshoy Karetny per. 19, Moscow, 127994, Russia
Summary:

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-diagonal 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.

2010 Mathematics Subject Classification. 60B20, 60G15.

Keywords: Wigner random matrix, Gaussian fluctuations, Gaussian free field.

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