Local semicircle law with imprimitive variance matrix
Probability
2013-11-11 v1
Abstract
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 . 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 , where the variances of the entries of may vary.
Cite
@article{arxiv.1311.2016,
title = {Local semicircle law with imprimitive variance matrix},
author = {Oskari Ajanki and Laszlo Erdos and Torben Krüger},
journal= {arXiv preprint arXiv:1311.2016},
year = {2013}
}