Matrix regularizing effects of Gaussian perturbations
Michael Aizenman, Ron Peled, Jeffrey Schenker, Mira Shamis, Sasha Sodin
Source record
Source: Crossref
Published: Apr 5, 2017
DOI: 10.1142/s0219199717500286
Open original source ↗Source abstract
The addition of noise has a regularizing effect on Hermitian matrices. This effect is studied here for [Formula: see text], where [Formula: see text] is the base matrix and [Formula: see text] is sampled from the GOE or the GUE random matrix ensembles. We bound the mean number of eigenvalues of [Formula: see text] in an interval, and present tail bounds for the distribution of the Frobenius and operator norms of [Formula: see text] and for the distribution of the norm of [Formula: see text] applied to a fixed vector. The bounds are uniform in [Formula: see text] and exceed the actual suprema by no more than multiplicative constants. The probability of multiple eigenvalues in an interval is also estimated.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.