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Resolvent convergence for sample covariance matrices with general covariance profiles and quadratic-form control

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arXiv:2109. 02644v5 Announce Type: replace-cross Abstract: We study the resolvent [ G^z = \left(\frac{1}{n}XX^T - zI_p\right)^{-1}, \qquad z\in\mathbb C,\ \Im(z)>0, ] where $X=(x_1,\ldots,x_n)\in\mathcal M_{p,n}$ is a random matrix with independent, but not necessarily identically distributed, columns.