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Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0
Random Matrices: Theory and Applications ( IF 0.9 ) Pub Date : 2019-03-25 , DOI: 10.1142/s2010326320500057
Xue Ding 1
Affiliation  

In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.

中文翻译:

当 p/n → 0 时,大四元数样本协方差矩阵和相关矩阵的 ESD 强收敛

在本文中,我们研究了大四元数样本协方差矩阵和相关矩阵的经验谱分布(ESD)的强收敛性,当总体维数[公式:见文本]与样本大小[公式:见文本]之比趋于零。我们证明了重整化四元数样本协方差矩阵的 ESD 几乎肯定会收敛到半圆定律。
更新日期:2019-03-25
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