For a class of unitarily invariant random matrices, eigenvalues of a rank-one perturbation converge to zeros of the Gaussian analytic function a minus sum c_k z^k, which also makes the critical outlier time scale optimal.
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Zeros Of Random Analytic Functions And Spectral Properties Of Perturbed Unitary Matrices
For a class of unitarily invariant random matrices, eigenvalues of a rank-one perturbation converge to zeros of the Gaussian analytic function a minus sum c_k z^k, which also makes the critical outlier time scale optimal.