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

Shuhua Chang and Yongcheng Qi

Statistics & Probability Letters, 2017, vol. 128, issue C, 8-13

Abstract: 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.

Keywords: Empirical spectral distribution; Spherical ensemble; Product ensemble; Random matrix (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2017.04.002

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