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arXiv · 1609.09096

Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

Yi Sun
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Abstract

We study multilevel matrix ensembles at general beta by identifying them with a class of processes defined via the branching rules for multivariate Bessel and Heckman-Opdam hypergeometric functions. For beta = 1, 2, we express the joint multilevel density of the eigenvalues of a generalized beta-Wishart matrix as a multivariate Bessel ensemble, generalizing a result of Dieker-Warren. In the null case, we prove the conjecture of Borodin-Gorin that the joint multilevel density of the beta-Jacobi ensemble is given by a principally specialized Heckman-Opdam measure.

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Yi Sun. 2016-09-28. Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures. https://arxiv.org/abs/1609.09096

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