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Inverse of a Sum of Random Matrices: A Dynamical Mean-Field Approach
We study $(\mathbf{O}^\top \mathbf{A} \mathbf{O} + \mathbf{B})^{-1}$, where $\mathbf{A}, \mathbf{B} \in \mathbb{R}^{N \times N}$ are symmetric positive definite, with limiting eigenvalue distributions ${\rm F}_{\mathbf{A}}, {\rm F}_{\mathbf{B}}$ and spectra bounded and bounded away from zero, and $\
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