The Airy_beta line ensemble is constructed for all beta>0 via explicit multi-time Laplace transform formulas, and it is shown to be the edge scaling limit of both the Dyson Brownian Motion and the Gaussian beta corners process.
Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures
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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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Airy$_\beta$ line ensemble and its Laplace transform
The Airy_beta line ensemble is constructed for all beta>0 via explicit multi-time Laplace transform formulas, and it is shown to be the edge scaling limit of both the Dyson Brownian Motion and the Gaussian beta corners process.