Titre :

Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble

Auteur(s) :

Gamboa, Fabrice [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Nagel, Jan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rouault, Alain [Auteur]
Laboratoire de Mathématiques de Versailles [LMV]

Discipline(s) HAL :

Mathématiques [math]
Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Théorie spectrale [math.SP]

Résumé en anglais : [en]

We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [18] for spectral measures of classical ensembles (Gauss-Hermite, ...
Lire la suite >We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [18] for spectral measures of classical ensembles (Gauss-Hermite, Laguerre, Jacobi) and it was extended to spectral matrix measures of the Hermite and Laguerre ensemble in [21]. In this paper, we consider the remaining case of spectral matrix measures of the Jacobi ensemble. Our main results are a large deviation principle for such measures and a sum rule for matrix measures with reference measure the Kesten-McKay law. As an important intermediate step, we derive the distribution of canonical moments of the matrix Jacobi ensemble.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL