Spectral Radii of Products of Random Rectangular Matrices

Yongcheng Qi () and Mengzi Xie ()
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Yongcheng Qi: University of Minnesota Duluth
Mengzi Xie: University of Minnesota Duluth

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 2185-2212

Abstract: 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 value 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 (J Theor Probab 30(1):326–364, 2017) when the rectangular matrices are square.

Keywords: Spectral radius; Eigenvalue; Random rectangular matrix; Non-Hermitian random matrix; 15B52; 60F99; 60G70; 62H10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00942-9

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