TY - JOUR

T1 - Empirical distribution of scaled eigenvalues for product of matrices from the spherical ensemble

AU - Chang, Shuhua

AU - Qi, Yongcheng

PY - 2017/9

Y1 - 2017/9

N2 - Consider the product of m independent n×n random matrices from the spherical ensemble for m≥1. The empirical distribution based on the n eigenvalues of the product is called the empirical spectral distribution. Two recent papers by Götze, Kösters and Tikhomirov (2015) and Zeng (2016) obtain the limit of the empirical spectral distribution for the product when m is a fixed integer. In this paper, we investigate the limiting empirical distribution of scaled eigenvalues for the product of m independent matrices from the spherical ensemble in the case when m changes with n, that is, m=mn is an arbitrary sequence of positive integers.

AB - Consider the product of m independent n×n random matrices from the spherical ensemble for m≥1. The empirical distribution based on the n eigenvalues of the product is called the empirical spectral distribution. Two recent papers by Götze, Kösters and Tikhomirov (2015) and Zeng (2016) obtain the limit of the empirical spectral distribution for the product when m is a fixed integer. In this paper, we investigate the limiting empirical distribution of scaled eigenvalues for the product of m independent matrices from the spherical ensemble in the case when m changes with n, that is, m=mn is an arbitrary sequence of positive integers.

KW - Empirical spectral distribution

KW - Product ensemble

KW - Random matrix

KW - Spherical ensemble

UR - http://www.scopus.com/inward/record.url?scp=85018775169&partnerID=8YFLogxK

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U2 - 10.1016/j.spl.2017.04.002

DO - 10.1016/j.spl.2017.04.002

M3 - Article

AN - SCOPUS:85018775169

VL - 128

SP - 8

EP - 13

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -