Local Laws and Edge Universality for Noncentral Sample Covariance Matrices

We consider the real noncentral sample covariance matrices $\mathcal{W}=YY^\top$ with $Y=A+Σ^{1/2}X$. Here $A\in\mathbb{R}^{M\times N}$ is deterministic, $Σ\in \mathbb{R}^{M\times M}$ is a deterministic positive definite population covariance matrix and $X\in\mathbb{R}^{M\times N}$ has independent c