Local semicircle law with imprimitive variance matrix

Oskari Ajanki, Lászlo Erdős, Torben Krüger
2014 Electronic Communications in Probability  
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.
doi:10.1214/ecp.v19-3121 fatcat:bdxansbg5jgf3a2lgnzhlrza5m