Matrix regularizing effects of Gaussian perturbations

@article{Aizenman2015MatrixRE,
title={Matrix regularizing effects of Gaussian perturbations},
author={M. Aizenman and R. Peled and J. Schenker and M. Shamis and S. Sodin},
journal={arXiv: Probability},
year={2015}
}

The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for $H=A+V$, where $A$ is the base matrix and $V$ is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of eigenvalues of $H$ in an interval, and present tail bounds for the distribution of the Frobenius and operator norms of $H^{-1}$ and for the distribution of the norm of $H^{-1}$ applied to a fixed vector. The bounds are uniform in $A$ and exceed the actualâ€¦Â Expand