Spectral Radii of Products of Random Rectangular Matrices

Yongcheng Qi, Mengzi Xie

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1 Scopus citations


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 languageEnglish (US)
Pages (from-to)2185-2212
Number of pages28
JournalJournal of Theoretical Probability
Issue number4
StatePublished - Dec 1 2020

Bibliographical note

Funding Information:
The authors would like to thank an anonymous referee for his/her careful reading of the manuscript. The research of Yongcheng Qi was supported in part by NSF Grant DMS-1916014.

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.


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


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