The anisotropic local law for sample covariance matrices under quadratic-form concentration

Renyuan Ma, Theodor Misiakiewicz

We study sample covariance matrices $K=\frac{1}{N}{\sum }_{i=1}^N{\mathbf{x}}_i{\mathbf{x}}_i^{\ast }\in {\mathbb{R}}^{n\times n}$ in the proportional regime $n\asymp N$. The columns $ \m…