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CLT for Linear Spectral Statistics of Wigner matrices (2009)

Bai, Zhidong; Northeast Normal University, Changchun; Baizd@nenu.edu.cn,
Wang, Xiaoying; Northeast Normal University, Changchun; Wangxy022@126.com,
Zhou, Wang; National University Of Singapore; Stazw@nus.edu.sg

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.

Publication details

Download	http://www.math.washington.edu/~ejpecp/viewarticle.php?id=2018
Publisher	Institute of Mathematical Statistics
Contributors	The first two authors were partially supported by CNSF 10871036 and NUS grant R-155-000-079-112 and the third author was partially supported by grant R-155-000-076-112 at the National University of Singapore
Repository	Electronic Journal of Probability (United States)
Keywords	15B52;60F15;62H99; Bernstein polynomial; central limit theorem; Stieltjes transform; Wigner matrices
Coverage	; ;