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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 100, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.100 (Mi sigma1995) 		 
Jacobi Beta Ensemble and $b$-Hurwitz Numbers

Giulio Ruzzaab

a Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande Edifício C6, 1749-016, Lisboa, Portugal
b Grupo de Física Matemática, Campo Grande Edifício C6, 1749-016, Lisboa, Portugal
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DOI: https://doi.org/10.3842/SIGMA.2023.100
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 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: beta ensembles, Jack polynomials, Hurwitz numbers, combinatorial maps.
Funding agency Grant number
Fundação para a Ciência e a Tecnologia 2022.07810.CEECIND
This work is supported by the FCT grant 2022.07810.CEECIND.
Received: July 3, 2023; in final form November 29, 2023; Published online December 19, 2023
Document Type: Article
MSC: 15B52, 05E05, 05E16
Language: English
Citation: Giulio Ruzza, “Jacobi Beta Ensemble and $b$-Hurwitz Numbers”, SIGMA, 19 (2023), 100, 18 pp.
Citation in format AMSBIB
\Bibitem{Ruz23}
\by Giulio~Ruzza
\paper Jacobi Beta Ensemble and $b$-Hurwitz Numbers
\jour SIGMA
\yr 2023
\vol 19
\papernumber 100
\totalpages 18
\mathnet{http://mi.mathnet.ru/sigma1995}
\crossref{https://doi.org/10.3842/SIGMA.2023.100}
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