Matrix regularizing effects of Gaussian perturbations

Michael Aizenman, Ron Peled, Jeffrey Schenker, Mira Shamis, Sasha Sodin

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Article number1750028
JournalCommunications in Contemporary Mathematics
Volume19
Issue number3
DOIs
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Gaussian perturbation
  • Minami estimate
  • Wegner estimate
  • deformed GOE
  • deformed GUE

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