### 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.

Original language | English (US) |
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Journal | Journal of Theoretical Probability |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

### Keywords

- Eigenvalue
- Non-Hermitian random matrix
- Random rectangular matrix
- Spectral radius

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## Cite this

Qi, Y., & Xie, M. (Accepted/In press). Spectral Radii of Products of Random Rectangular Matrices.

*Journal of Theoretical Probability*. https://doi.org/10.1007/s10959-019-00942-9