CLT for linear spectral statistics of Wigner matrices. (English) Zbl 1188.15032

Bai, Zhidong; Wang, Xiaoying; Zhou, Wang

Electron. J. Probab. 14, 2391-2417 (2009).

Summary: 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.

MSC:

15B52	Random matrices (algebraic aspects)
60F05	Central limit and other weak theorems
60G15	Gaussian processes

Keywords:

Bernstein polynomial; central limit theorem (CLT); Stieltjes transform; Wigner matrices; linear spectral statistics; semicircle law; Gaussian process