Random matrices: overcrowding estimates for the spectrum
classification
🧮 math.PR
keywords
matricesrandomestimatesovercrowdingaddressarbitraryboundscases
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We address overcrowding estimates for the singular values of random iid matrices, as well as for the eigenvalues of random Wigner matrices. We show evidence of long range separation under arbitrary perturbation even in matrices of discrete entry distributions. In many cases our method yields nearly optimal bounds
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