Spectral deconvolution of unitarily invariant matrix models
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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.
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