Jacobi Beta Ensemble and -Hurwitz Numbers

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Author: Ruzza, Giulio
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212031
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Jacobi Beta Ensemble and -Hurwitz Numbers. Giulio Ruzza. SIGMA 19 (2023), 100, 18 pages

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 Dołęga. The proof relies on Kadell's generalization of the Selberg integral. The Laguerre limit is also considered. All the relevan...