Matrix Models for Multilevel Heckman-opdam and Multivariate Bessel Measures
نویسنده
چکیده
We study multilevel matrix ensembles at general β by identifying them with a class of processes defined via the branching rules for multivariate Bessel and Heckman-Opdam hypergeometric functions. For β = 1, 2, we express the joint multilevel density of the eigenvalues of a generalized Wishart matrix as a multivariate Bessel ensemble, generalizing a result of Dieker-Warren in [DW09]. In the null case, we prove the conjecture of Borodin-Gorin in [BG13] that the joint multilevel density of the β-Jacobi ensemble is given by a principally specialized Heckman-Opdam measure.
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