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Limiting Empirical Spectral Distribution for Products of Rectangular Matrices (2104.03244v1)
Published 7 Apr 2021 in math.PR
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.