Phase transition for the smallest eigenvalue of covariance matrices

Zhigang Bao, Jaehun Lee, Xiaocong Xu

In this paper, we study the smallest non-zero eigenvalue of the sample covariance matrices $\mathcal{S}(Y)=Y{Y}^{\ast }$, where $Y=(y_{ij})$ is an $M\times N$ matrix with iid mean $0$ vari…