Local Law and Outlier Eigenvalues of Spiked Separable Covariance Matrices

Zhili Wang, Bin Qin

We prove local laws for the resolvents of separable covariance matrices of the form $\mathcal{Q}=A^{1/2}XB{X}^{\ast }{A}^{1/2}$, where $X=(x_{ij})$ is a $p\times n$ random matrix whose entrie…