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

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  • Chang, Shuhua
  • Qi, Yongcheng

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.

Suggested Citation

  • Chang, Shuhua & Qi, Yongcheng, 2017. "Empirical distribution of scaled eigenvalues for product of matrices from the spherical ensemble," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 8-13.
    • Handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:8-13
    DOI: 10.1016/j.spl.2017.04.002
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    Cited by:

    1. Yu Miao & Yongcheng Qi, 2021. "Limiting Spectral Radii of Circular Unitary Matrices Under Light Truncation," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2145-2165, December.
    2. Yongcheng Qi & Mengzi Xie, 2020. "Spectral Radii of Products of Random Rectangular Matrices," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2185-2212, December.

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