Jacobi Beta Ensemble and $b$-Hurwitz Numbers
Mathematical Physics
2024-05-09 v3 Combinatorics
math.MP
Abstract
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 Dolega. 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 Dolega) in terms of colored monotone Hurwitz maps.
Cite
@article{arxiv.2306.16323,
title = {Jacobi Beta Ensemble and $b$-Hurwitz Numbers},
author = {Giulio Ruzza},
journal= {arXiv preprint arXiv:2306.16323},
year = {2024}
}