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

Fabrice Gamboa (1) , Jan Nagel (2) , Alain Rouault (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 LMV - Laboratoire de Mathématiques de Versailles

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.

Domaines: Mathématiques [math]; Probabilités [math.PR]; Théorie spectrale [math.SP]

Fabrice Gamboa, Jan Nagel, Alain Rouault. Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble. 2018. ⟨hal-01925648⟩