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.
Citation
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
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