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arXiv · 1811.06311

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

Fabrice Gamboa·Jan Nagel·Alain Rouault
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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.

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Fabrice Gamboa, Jan Nagel, Alain Rouault. 2018-11-15. Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble. https://arxiv.org/abs/1811.06311

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