We establish that the limiting spectral distribution of a block-rescaled empirical covariance matrix is an arcsine law when the ratio between the dimension and the underlying sample size converges to 1 and when the samples corresponding to each block are independent. We further propose a conjecture for the cases where the latter ratio converges to a constant in the unit interval.

翻译：我们确认,当尺寸与底部样本大小之间的比重接近1时,当每个区块对应的样本是独立的时,区块重新标定的经验共变矩阵的有限光谱分布是一种弧法。 我们还为后一比率在单位间隔内与常数相融合的情况提出一个推测。