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Large deviations and a new sum rule for spectral matrix measures of the Jacobi ensemble
Random Matrices: Theory and Applications ( IF 0.9 ) Pub Date : 2019-10-22 , DOI: 10.1142/s2010326321500088
Fabrice Gamboa 1 , Jan Nagel 2 , Alain Rouault 3
Affiliation  

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.

中文翻译:

Jacobi 系综谱矩阵测度的大偏差和新的求和规则

我们继续探索来自随机矩阵理论和求和规则的对象的大偏差之间的联系。这种联系是在 [Sum rules via large deviations, J. Funct. 肛门。270(2) (2016) 509–559] 用于经典系综(Gauss-Hermite、Laguerre、Jacobi)的光谱测量,并在 [Sum rules and large deviations forspectrum matrix 中扩展到 Hermite 和 Laguerre 系综的光谱矩阵测量措施,伯努利 25(1) (2018) 712–741]。在本文中,我们考虑 Jacobi 系综的谱矩阵测量的剩余情况。我们的主要结果是此类度量的大偏差原则和矩阵度量的求和规则以及参考度量 Kesten-McKay 定律。作为一个重要的中间步骤,我们推导了 Jacobi 系综的矩阵规范矩的分布。
更新日期:2019-10-22
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