We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulae for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.
Bibliographical noteFunding Information:
We thank M. Bertola and D. Yang for valuable conversations. This project has received funding from the European Union’s H2020 research and innovation programme under the Marie Skłodowska–Curie grant No. 778010 IPaDEGAN. The research of G.R. is supported by the Fonds de la Recherche Scientifique-FNRS under EOS project O013018F.
Open access funding provided by Scuola Internazionale Superiore di Studi Avanzati - SISSA within the CRUI-CARE Agreement.
© 2021, The Author(s).
- Jacobi ensemble
- Hurwitz numbers
- multi-point correlators