Large deviations for the largest eigenvalue of the sum of two random matrices

Guionnet, Alice; Maïda, Mylène

Type de document :

Compte-rendu et recension critique d'ouvrage

Titre :

Large deviations for the largest eigenvalue of the sum of two random matrices

Auteur(s) :

Guionnet, Alice [Auteur]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Centre National de la Recherche Scientifique [CNRS]
Maïda, Mylène [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Electronic Journal of Probability

Pagination :

Éditeur :

Institute of Mathematical Statistics (IMS)

Date de publication :

2020-02-05

ISSN :

1083-6489

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

In this paper, we consider the addition of two matrices in generic position, namely A + U BU * , where U is drawn under the Haar measure on the unitary or the orthogonal group. We show that, under mild conditions on the ...
Lire la suite >In this paper, we consider the addition of two matrices in generic position, namely A + U BU * , where U is drawn under the Haar measure on the unitary or the orthogonal group. We show that, under mild conditions on the empirical spectral measures of the deterministic matrices A and B, the law of the largest eigenvalue satisfies a large deviation principle, in the scale N, with an explicit rate function involving the limit of spherical integrals. We cover in particular all the cases when A and B have no outliers.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Community of mathematics and fundamental computer science in Lyon

Collections :