Translator Disclaimer
dec 2005 On the convergence of the spectral empirical process of Wigner matrices
Z.D. Bai, J. Yao
Author Affiliations +
Bernoulli 11(6): 1059-1092 (dec 2005). DOI: 10.3150/bj/1137421640


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.


Download Citation

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


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


Vol.11 • No. 6 • dec 2005
Back to Top