论文标题
单位不变矩阵模型的光谱反卷积
Spectral deconvolution of unitarily invariant matrix models
论文作者
论文摘要
本文在假设噪声的分布是单位不变的，实现了一种复杂的分析方法，以通过添加或随机矩阵噪声的添加或乘法恢复矩阵的频谱。 Arizmendi，Tarrago和Vargas在Arxiv中引入的方法：1711.08871，分为两个步骤：第一步是通过固定点方法组成的，以计算某个域中所需分布的stieltjes变换，第二步是第二步，第二步是由cauchy分布依赖于噪声的cauchy分布的经典反向扭转的频率。我们还为第一步的平方误差提供明确的界限。
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.
