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Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

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.

preprint2016arXivOpen access
Yi Sun
math.RTmath-phmath.PRmath.MP
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Open access1 author4 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Yi Sun

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