论文标题
扰动分解方法：通过扰动理论的随机矩阵集合的光谱密度
The Perturbative Resolvent Method: spectral densities of random matrix ensembles via perturbation theory
论文作者
论文摘要
我们提出了一种简单的扰动方法，用于计算热力学极限中随机矩阵集合的光谱密度，我们称为扰动分解方法（PRM）。 PRM基于构建方程的线性系统，并计算使用零温腔法对小扰动的响应来响应这些方程的解决方案。我们通过提供对称矩阵的Wigner半圆形定律的简单分析推导，即Wishart矩阵的Marchenko-Pastur定律，由两个正方形矩阵组成的产品的频谱密度以及实际随机矩阵的圆和椭圆法。
We present a simple, perturbative approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit we call the Perturbative Resolvent Method (PRM). The PRM is based on constructing a linear system of equations and calculating how the solutions to these equation change in response to a small perturbation using the zero-temperature cavity method. We illustrate the power of the method by providing simple analytic derivations of the Wigner Semi-circle Law for symmetric matrices, the Marchenko-Pastur Law for Wishart matrices, the spectral density for a product Wishart matrix composed of two square matrices, and the Circle and elliptic laws for real random matrices.
