单一无变动矩阵模型的光谱分解变异 (Spectral deconvolution of unitarily invariant matrix models)

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.

翻译：本文件采用复杂的分析方法,在假定噪音的分布是整体变化的假设下,通过随机矩阵噪音的增加或倍增来恢复受随机矩阵噪音所扰动的矩阵频谱,Arizmendi、Tarrago和Vargas在ArXiv:1711.08871中采用的这种方法分两步进行:第一步是用固定点法计算Stieltjes在某一域内所希望的分布的变形,第二步是古老的Cauchy分布的变形,其参数取决于噪音的强度。我们还为第一步的平均平方错误提供了明确的界限。