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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Chang, Shuhua¹  Li, Deli²  Qi, Yongcheng³ 

[1] Tianjin Univ Finance & Econ, Coordinated Innovat Ctr Computable Modeling Manag, Tianjin 300222, Peoples R China

[2] Lakehead Univ, Dept Math Sci, Thunder Bay, ON P7B 5E1, Canada

[3] Univ Minnesota, Dept Math & Stat, 1117 Univ Dr, Duluth, MN 55812 USA

关键词: Limiting distribution;    Spectral radius;    Spherical ensemble;    Product ensemble;    Random matrix;   

DOI  :  10.1016/j.jmaa.2018.01.048

来源: Elsevier

【 摘 要 】

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 = m(n) tends to infinity as n goes to infinity, we show that the logarithmic spectral radii have a normal limit. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free