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

Guionnet, Alice; Maïda, Mylène

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

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

Author(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]

Journal title :

Electronic Journal of Probability

Pages :

Publisher :

Institute of Mathematical Statistics (IMS)

Publication date :

2020-02-05

ISSN :

1083-6489

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Community of mathematics and fundamental computer science in Lyon

Collections :