Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Tamara Grava; Giulio Ruzza; Massimo Gisonni

doi:10.1007/s11005-021-01396-z

Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Tamara Grava, Giulio Ruzza, Massimo Gisonni

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Abstract

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 language	English
Article number	67
Journal	Letters in Mathematical Physics
Volume	111
Issue number	3
Early online date	12 May 2021
DOIs	https://doi.org/10.1007/s11005-021-01396-z
Publication status	Published - 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).

Keywords

Jacobi ensemble
Hurwitz numbers
multi-point correlators

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Cite this

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title = "Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials",

abstract = "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.",

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author = "Tamara Grava and Giulio Ruzza and Massimo Gisonni",

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doi = "10.1007/s11005-021-01396-z",

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AU - Grava, Tamara

AU - Ruzza, Giulio

AU - Gisonni, Massimo

N1 - 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).

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N2 - 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.

AB - 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.

KW - Jacobi ensemble

KW - Hurwitz numbers

KW - multi-point correlators

U2 - 10.1007/s11005-021-01396-z

DO - 10.1007/s11005-021-01396-z

M3 - Article (Academic Journal)

VL - 111

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 3

M1 - 67

ER -

Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Abstract

Bibliographical note

Keywords

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