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We study additive finite-rank perturbations of random periodic band matrices under the assumption that the nontrivial eigenvalues of the perturbation do not depend on the dimension.
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by same author, Finite-rank perturbations of random band matrices via infinitesimal free probability , Comm. Pure Appl. Math. 74
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by same author, The outliers of a deformed Wigner matrix , Ann. Probab. 42
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