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We study the resolvent \(G^z=\left(\frac{1}{n}XX^{\top}-zI_p\right)^{-1}\), where \(z\in\mathbb{C}\) satisfies \(\Im(z)>0\) and \(X=(x_1,\ldots,x_n)\in\mathbb{R}^{p\times n}\) is a random matrix with independent, but not necessarily identically distributed, columns.
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