Electronic Journal of Probability

CLT for Linear Spectral Statistics of Wigner matrices

Zhidong Bai, Xiaoying Wang, and Wang Zhou

Full-text: Open access

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

Permanent link to this document
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

Keywords
Bernstein polynomial central limit theorem Stieltjes transform Wigner matrices

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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