Large deviations and a new sum rule for spectral matrix measures of the Jacobi ensemble
In: Random Matrices: Theory and Applications Random Matrices: Theory and Applications, 2021, 10 (1), ⟨10.1142/S2010326321500088⟩ Random Matrices: Theory and Applications, World Scientific, 2021, 10 (1), ⟨10.1142/S2010326321500088⟩; (2021)
Online
unknown
Zugriff:
International audience; We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509-559] 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 [Sum rules and large deviations for spectral matrix measures, Bernoulli 25(1) (2018) 712-741]. 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 matricial canonical moments of the Jacobi ensemble.
| Titel: |
Large deviations and a new sum rule for spectral matrix measures of the Jacobi ensemble
|
|---|---|
| Autor/in / Beteiligte Person: | Gamboa, Fabrice ; Rouault, Alain ; Nagel, Jan ; Institut de Mathématiques de Toulouse UMR5219 (IMT) ; Université Toulouse Capitole (UT Capitole) ; Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) ; Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J) ; Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3) ; Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) ; Fakultät für Mathematik [Dortmund] ; Laboratoire de Mathématiques de Versailles (LMV) ; Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) ; Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) ; Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1) ; Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3) ; Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS) |
| Link: | |
| Quelle: | Random Matrices: Theory and Applications Random Matrices: Theory and Applications, 2021, 10 (1), ⟨10.1142/S2010326321500088⟩ Random Matrices: Theory and Applications, World Scientific, 2021, 10 (1), ⟨10.1142/S2010326321500088⟩; (2021) |
| Veröffentlichung: | HAL CCSD, 2021 |
| Medientyp: | unknown |
| ISSN: | 2010-3263 (print) |
| Schlagwort: |
|
| Sonstiges: |
|