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

2018/11/15 by Gamboa, Fabrice, Nagel, Jan, Rouault, Alain
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1811.06311

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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