Eigenvectors of a matrix under random perturbation

Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl

Published 2018-01-31Version 1

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.