Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble
Probability
2018-11-16 v1
Abstract
We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [17] 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 [20]. 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.
Keywords
Cite
@article{arxiv.1811.06311,
title = {Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble},
author = {Fabrice Gamboa and Jan Nagel and Alain Rouault},
journal= {arXiv preprint arXiv:1811.06311},
year = {2018}
}