Local semicircle law with imprimitive variance matrix
نویسندگان
چکیده
We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue −1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X∗X, where the variances of the entries of X may vary.
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تاریخ انتشار 2014