Eigenvectors of a matrix under random perturbation

2018/01/31 by Florent Benaych-Georges, Benaych-Georges, Florent, Nathanaël Enriquez +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1801.10512

15 pages, 3 figures. To appear in RMTA

arxiv created 2020/03/17 · arxiv updated 2020/03/19

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.

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