Matrix regularizing effects of Gaussian perturbations

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

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
Issue number3
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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


Dive into the research topics of 'Matrix regularizing effects of Gaussian perturbations'. Together they form a unique fingerprint.

Cite this