## Electronic Journal of Probability

### CLT for Linear Spectral Statistics of Wigner matrices

#### Abstract

In this paper, we prove that the spectral empirical process of Wigner matrices under sixth-moment conditions, which is indexed by a set of functions with continuous fourth-order derivatives on an open interval including the support of the semicircle law, converges weakly in finite dimensions to a Gaussian process.

#### Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 83, 2391-2417.

Dates
Accepted: 1 November 2009
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819544

Digital Object Identifier
doi:10.1214/EJP.v14-705

Mathematical Reviews number (MathSciNet)
MR2556016

Zentralblatt MATH identifier
1188.15032

Subjects
Primary: 15B52: Random matrices
Secondary: 60F15: Strong theorems 62H99: None of the above, but in this section

Rights

#### Citation

Bai, Zhidong; Wang, Xiaoying; Zhou, Wang. CLT for Linear Spectral Statistics of Wigner matrices. Electron. J. Probab. 14 (2009), paper no. 83, 2391--2417. doi:10.1214/EJP.v14-705. https://projecteuclid.org/euclid.ejp/1464819544

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