Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Tamara Grava, Giulio Ruzza, Massimo Gisonni

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
Original languageEnglish
Article number67
JournalLetters in Mathematical Physics
Issue number3
Early online date12 May 2021
Publication statusPublished - Jun 2021

Bibliographical note

Funding 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.

Funding Information:
Open access funding provided by Scuola Internazionale Superiore di Studi Avanzati - SISSA within the CRUI-CARE Agreement.

Publisher Copyright:
© 2021, The Author(s).


  • Jacobi ensemble
  • Hurwitz numbers
  • multi-point correlators


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