Deterministic equivalence for noisy perturbations
Spectral Theory
2020-01-27 v1 Probability
Abstract
We prove a quantitative deterministic equivalence theorem for the logarithmic potentials of deterministic complex matrices subject to small random perturbations. We show that with probability close to this log-potential is, up to a small error, determined by the singular values of the unperturbed matrix which are larger than some small -dependent cut-off parameter.
Cite
@article{arxiv.2001.09024,
title = {Deterministic equivalence for noisy perturbations},
author = {Martin Vogel and Ofer Zeitouni},
journal= {arXiv preprint arXiv:2001.09024},
year = {2020}
}