Limiting Empirical Spectral Distribution for Products of Rectangular Matrices
Limiting Empirical Spectral Distribution for Products of Rectangular Matrices
复制标题
DOI：
10.1016/j.jmaa.2021.125237
复制
发表时间：
2021-04
影响因子：
1.3
通讯作者：
Y. Qi;Hongru Zhao
中科院分区：
文献类型：
--
作者：
Y. Qi;Hongru Zhao
本文讨论了元素为独立同分布标准复高斯随机变量的相依随机矩形矩阵，并假设它们的乘积为n × n方阵。本文研究了乘积矩阵维数趋于无穷大时乘积的极限经验谱分布，并且m可能随乘积矩阵维数的变化而发散.我们给出了一个完整的描述的极限分布的经验谱分布的乘积矩阵，并说明了一些例子。
In this paper, we considermindependent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of themrectangular matrices is annbynsquare matrix. We study the limiting empirical spectral distributions of the product where the dimension of the product matrix goes to infinity, andmmay change with the dimension of the product matrix and diverge. We give a complete description for the limiting distribution of the empirical spectral distributions for the product matrix and illustrate some examples.