Spectral Radii of Products of Random Rectangular Matrices

Yongcheng Qi, Mengzi Xie

Research output: Contribution to journalArticle

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 languageEnglish (US)
JournalJournal of Theoretical Probability
DOIs
StateAccepted/In press - Jan 1 2019

Keywords

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

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