Eigenvectors of a matrix under random perturbation

Abstract : In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent, centered, with a variance profile. This is done through a perturbative expansion of spectral measures associated to the state defined by a given vector.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01705890
Contributor : Florent Benaych-Georges <>
Submitted on : Saturday, February 10, 2018 - 3:01:45 AM
Last modification on : Tuesday, November 19, 2019 - 9:29:01 AM

Links full text

Identifiers

  • HAL Id : hal-01705890, version 1
  • ARXIV : 1801.10512

Citation

Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl. Eigenvectors of a matrix under random perturbation. 2018. ⟨hal-01705890⟩

Share

Metrics

Record views

250