Jacobi Beta Ensemble and $b$-Hurwitz Numbers

Abstract

We express correlators of the Jacobi $\beta$ ensemble in terms of (a special case of) $b$-Hurwitz numbers, a deformation of Hurwitz numbers recently introduced by Chapuy and Dolega. 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 Dolega) in terms of colored monotone Hurwitz maps.

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Cited by in corpus (1)

• Matrix models for extremal and integrated correlators of higher rank