Eigenvectors of a matrix under random perturbation
Probability
2020-03-19 v5
Abstract
In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of 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.
Cite
@article{arxiv.1801.10512,
title = {Eigenvectors of a matrix under random perturbation},
author = {Florent Benaych-Georges and Nathanaël Enriquez and Alkéos Michaïl},
journal= {arXiv preprint arXiv:1801.10512},
year = {2020}
}
Comments
15 pages, 3 figures. To appear in RMTA