Jacobi Beta Ensemble and 𝑏-Hurwitz Numbers

Abstract

We express correlators of the Jacobi 𝛽 ensemble in terms of (a special case of) 𝑏-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 𝑏-Hurwitz numbers are interpreted (following Bonzom, Chapuy, and Dołęga) in terms of colored monotone Hurwitz maps.