2021
DOI: 10.48550/arxiv.2106.04785
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Quantitative results for non-normal matrices subject to random and deterministic perturbations

Abstract: We consider the eigenvalue distribution of a fixed matrix subject to a small perturbation. In particular, we prove quantitative comparison results which show that the logarithmic potential is stable under perturbations with small norm or low rank, provided the smallest and largest singular values are not too extreme. We also establish a quantitative version of the Tao-Vu replacement principle. As an application of our results, we study the spectral distribution of banded Toeplitz matrices subject to small rand… Show more

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