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.
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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

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


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



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