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.
Type de document :
Pré-publication, Document de travail
MAP5 2018-03. 11 pages, 2 figures. 2018
Domaine :

https://hal.archives-ouvertes.fr/hal-01705890
Contributeur : Florent Benaych-Georges <>
Soumis le : samedi 10 février 2018 - 03:01:45
Dernière modification le : mercredi 4 juillet 2018 - 23:14:02

Identifiants

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

Citation

Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl. Eigenvectors of a matrix under random perturbation. MAP5 2018-03. 11 pages, 2 figures. 2018. 〈hal-01705890〉

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