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We extend the proof of the local semicircle law for generalized Wigner matrices given in  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.doi:10.1214/ecp.v19-3121 fatcat:bdxansbg5jgf3a2lgnzhlrza5m