@article{0c99200b2fc2497d986ad4e894b65610,

title = "Matrix regularizing effects of Gaussian perturbations",

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.",

keywords = "Gaussian perturbation, Minami estimate, Wegner estimate, deformed GOE, deformed GUE",

author = "Michael Aizenman and Ron Peled and Jeffrey Schenker and Mira Shamis and Sasha Sodin",

note = "Publisher Copyright: {\textcopyright} 2017 World Scientific Publishing Company.",

year = "2017",

month = jun,

day = "1",

doi = "10.1142/S0219199717500286",

language = "אנגלית",

volume = "19",

journal = "Communications in Contemporary Mathematics",

issn = "0219-1997",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}