Matrix regularizing effects of Gaussian perturbations
Communications in Contemporary Mathematics
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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.
AuthorsAizenman, M; Peled, R; Schenker, J; Shamis, M; SODIN, A
- Applied Mathematics