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|Abstract:||The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for H = A + V, where A is the base matrix and V is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of eigenvalues of H in an interval, and present tail bounds for the distribution of the Frobenius and operator norms of H-1 and for the distribution of the norm of H-1 applied to a fixed vector. The bounds are uniform in A and exceed the actual suprema by no more than multiplicative constants. The probability of multiple eigenvalues in an interval is also estimated.|
|Electronic Publication Date:||9-Mar-2017|
|Citation:||Aizenman, Michael, Peled, Ron, Schenker, Jeffrey, Shamis, Mira, Sodin, Sasha. (2017). Matrix regularizing effects of Gaussian perturbations. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 19 (10.1142/S0219199717500286|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||COMMUNICATIONS IN CONTEMPORARY MATHEMATICS|
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