Limiting distributions of spectral radii for product of matrices from the spherical ensemble

Shuhua Chang, Deli Li, Yongcheng Qi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Consider the product of m independent n×n random matrices from the spherical ensemble for m≥1. The spectral radius is defined as the maximum absolute value of the n eigenvalues of the product matrix. When m=1, the limiting distribution for the spectral radii has been obtained by Jiang and Qi (2017). In this paper, we investigate the limiting distributions for the spectral radii in general. When m is a fixed integer, we show that the spectral radii converge weakly to distributions of functions of independent Gamma random variables. When m=mn tends to infinity as n goes to infinity, we show that the logarithmic spectral radii have a normal limit.

Original languageEnglish (US)
Pages (from-to)1165-1176
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume461
Issue number2
DOIs
StatePublished - May 15 2018

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Spectral Radius
Limiting Distribution
Ensemble
Random variables
Infinity
Matrix Product
Random Matrices
Absolute value
Logarithmic
Random variable
Tend
Eigenvalue
Converge
Integer

Keywords

  • Limiting distribution
  • Product ensemble
  • Random matrix
  • Spectral radius
  • Spherical ensemble

Cite this

Limiting distributions of spectral radii for product of matrices from the spherical ensemble. / Chang, Shuhua; Li, Deli; Qi, Yongcheng.

In: Journal of Mathematical Analysis and Applications, Vol. 461, No. 2, 15.05.2018, p. 1165-1176.

Research output: Contribution to journalArticle

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