In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population model as a special case. Meanwhile, the number of the spiked eigenvalues can either be fixed or grow to infinity. It is seen from our theorems that the divergence of population spectral norm affects the fluctuations of the linear spectral statistics in a fickle way, depending on the divergence rate.

翻译：在本文中,我们根据不同的光谱规范人口模型,为高维样本共变矩阵的某些光谱统计设定了新的中央限值理论。这个模型作为一个特例覆盖了不同的悬浮人口模型。与此同时,高涨的乙基值的数量可以固定,也可以增长到无限。从我们的理论中可以看出,人口光谱规范的差异会以变化不定的方式影响线性光谱统计的波动,取决于差异率。