This article is cited in 29 papers

CLT for spectra of submatrices of Wigner random matrices

Alexei Borodin<sup>ab

a</sup> IITP RAS, Bolshoy Karetny per. 19, Moscow, 127994, Russia
^b Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139, USA

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-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.

Key words and phrases: Wigner random matrix, Gaussian fluctuations, Gaussian Free Field.

MSC: 60B20, 60G15

Received: October 5, 2010; in revised form June 15, 2013

Language: English

DOI: 10.17323/1609-4514-2014-14-1-29-38

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