Please use this identifier to cite or link to this item: https://doi.org/10.3150/bj/1137421640
Title: On the convergence of the spectral empirical process of Wigner matrices
Authors: Bai, Z.D. 
Yao, J.
Keywords: Central limit theorem
Linear spectral statistics
Random matrix
Spectral distribution
Wigner matrices
Issue Date: Dec-2005
Citation: Bai, Z.D., Yao, J. (2005-12). On the convergence of the spectral empirical process of Wigner matrices. Bernoulli 11 (6) : 1059-1092. ScholarBank@NUS Repository. https://doi.org/10.3150/bj/1137421640
Abstract: 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. © 2005 ISI/BS.
Source Title: Bernoulli
URI: http://scholarbank.nus.edu.sg/handle/10635/105269
ISSN: 13507265
DOI: 10.3150/bj/1137421640
Appears in Collections:Staff Publications

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