Central limit theorem for eigenvalue statistics of sample covariance matrix with random population

Ji Oon Lee, Yiting Li

Consider the sample covariance matrix $${\Sigma }^{1/2}X{X}^T{\Sigma }^{1/2}$$ where $X$ is an $M\times N$ random matrix with independent entries and $\Sigma$ is an $M\times M$ diagonal matrix. It is kno…