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dec 2005 On the convergence of the spectral empirical process of Wigner matrices
Z.D. Bai, J. Yao
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Bernoulli 11(6): 1059-1092 (dec 2005). DOI: 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.

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Z.D. Bai. J. Yao. "On the convergence of the spectral empirical process of Wigner matrices." Bernoulli 11 (6) 1059 - 1092, dec 2005. https://doi.org/10.3150/bj/1137421640

Information

Published: dec 2005
First available in Project Euclid: 16 January 2006

zbMATH: 1101.60012
MathSciNet: MR2189081
Digital Object Identifier: 10.3150/bj/1137421640

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

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Vol.11 • No. 6 • dec 2005
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