Limiting Empirical Spectral Distribution for Products of Rectangular Matrices

Yongcheng Qi; Hongru Zhao

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arXiv · 2104.03244

Limiting Empirical Spectral Distribution for Products of Rectangular Matrices

Yongcheng Qi·Hongru Zhao

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Abstract

In this paper, we consider $m$ independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the $m$ rectangular matrices is an $n$ by $n$ square matrix. We study the limiting empirical spectral distributions of the product where the dimension of the product matrix goes to infinity, and $m$ may 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.

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Yongcheng Qi, Hongru Zhao. 2021-04-07. Limiting Empirical Spectral Distribution for Products of Rectangular Matrices. https://arxiv.org/abs/2104.03244

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