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

Shuhua Chang, Deli Li, Yongcheng Qi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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

Keywords

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

Fingerprint Dive into the research topics of 'Limiting distributions of spectral radii for product of matrices from the spherical ensemble'. Together they form a unique fingerprint.

Cite this