Jacobi Beta Ensemble and -Hurwitz Numbers - Ruzza, Giulio (Symmetry, Integrability and Geometry: Methods and Applications, 2023)
We express correlators of the Jacobi ensemble in terms of (a special case of) -Hurwitz numbers, a deformation of Hurwitz numbers recently introduced by Chapuy and Dołęga. The proof relies on Kadell's generalization of the Selberg integral. The Laguerre limit is also considered. All the relevant -Hurwitz numbers are interpreted (following Bonzom, Chapuy, and Dołęga) in terms of colored monotone Hurwitz maps.