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Jacobi Beta Ensemble and $b$-Hurwitz Numbers
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 Dołȩga. 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 Dołȩga) in terms of colored monotone Hurwitz maps.
Keywords: Jack polynomials, Hurwitz numbers, combinatorial maps.
Mots-clés : beta ensembles 
@article{SIGMA_2023_19_a99,
     author = {Giulio Ruzza},
     title = {Jacobi {Beta} {Ensemble} and $b${-Hurwitz} {Numbers}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2023},
     volume = {19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a99/}
}
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Giulio Ruzza. Jacobi Beta Ensemble and $b$-Hurwitz Numbers. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a99/

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