It is well known that the spectral distribution Fn of a Wigner matrix converges to Wigner's semicircle law. We consider the empirical process indexed by a set of functions analytic on an open domain of the complex plane including the support of the semicircle law. Under fourth-moment conditions, we prove that this empirical process converges to a Gaussian process. Explicit formulae for the mean function and the covariance function of the limit process are provided.
Publié le : 2005-12-14
Classification:
central limit theorem,
linear spectral statistics,
random matrix,
spectral distribution,
Wigner matrices
@article{1137421640,
author = {Bai, Z.D. and Yao, J.},
title = {On the convergence of the spectral empirical process of Wigner matrices},
journal = {Bernoulli},
volume = {11},
number = {1},
year = {2005},
pages = { 1059-1092},
language = {en},
url = {http://dml.mathdoc.fr/item/1137421640}
}
Bai, Z.D.; Yao, J. On the convergence of the spectral empirical process of Wigner matrices. Bernoulli, Tome 11 (2005) no. 1, pp. 1059-1092. http://gdmltest.u-ga.fr/item/1137421640/