标题： 多层Heckman-Opdam和多变量Bessel测度的矩阵模型 显示英文标题

标题： Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

摘要： 我们通过将多级矩阵系综与通过多变量贝塞尔和赫克曼-奥普达姆超几何函数的分支规则定义的过程相联系，研究一般beta下的多级矩阵系综。 对于beta = 1, 2，我们将广义beta-Wishart矩阵的特征值的联合多级密度表示为多变量贝塞尔系综，推广了Dieker-Warren的结果。 在零假设情况下，我们证明了Borodin-Gorin的猜想，即beta-Jacobi系综的联合多级密度由主要特化的Heckman-Opdam测度给出。 显示英文摘要

摘要： 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.