Spectral deconvolution of unitarily invariant matrix models
Abstract
The present paper implements a complex analytic method to recover the spectrum of a matrix perturbed by either the addition or the multiplication of a random matrix noise, under the assumption that the distribution of the noise is unitarily invariant. This method, introduced by Arizmendi, Tarrago and Vargas in arXiv:1711.08871, is done in two steps : the first step consists in a fixed point method to compute the Stieltjes transform of the desired distribution in a certain domain, and the second step is a classical deconvolution by a Cauchy distribution, whose parameter depends on the intensity of the noise. We also provide explicit bounds for the mean squared error of the first step.
Cite
@article{arxiv.2006.09356,
title = {Spectral deconvolution of unitarily invariant matrix models},
author = {Pierre Tarrago},
journal= {arXiv preprint arXiv:2006.09356},
year = {2020}
}
Comments
Version 2 : minor changes, references added and improved presentation. 60 pages, 4 figures