Spectral Radii of Products of Random Rectangular Matrices

Yongcheng Qi; Mengzi Xie

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arXiv · 1909.04845

Spectral Radii of Products of Random Rectangular Matrices

Yongcheng Qi·Mengzi Xie

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Abstract

We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of the m rectangular matrices is an n by n square matrix. The maximum absolute values of the n eigenvalues of the product matrix is called spectral radius. In this paper, we study the limiting spectral radii of the product when m changes with n and can even diverge. We give a complete description for the limiting distribution of the spectral radius. Our results reduce to those in Jiang and Qi [26] when the rectangular matrices are square ones.

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Yongcheng Qi, Mengzi Xie. 2019-09-11. Spectral Radii of Products of Random Rectangular Matrices. https://arxiv.org/abs/1909.04845

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