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.
Bibliographical noteFunding Information:
The authors would like to thank an anonymous referee for his/her careful reading of the manuscript and suggestion which has improved the layout of the manuscript. The research of Yongcheng Qi was supported in part by NSF Grant DMS-1916014 .
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- Empirical spectral distribution
- Non-Hermitian random matrix
- Product of rectangular matrices