Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Tamara Grava; Giulio Ruzza; Massimo Gisonni

Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

Tamara Grava, Giulio Ruzza, Massimo Gisonni

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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
Journal	Letters in Mathematical Physics
Publication status	Accepted/In press - 2021

Keywords

Jacobi ensemble
Hurwitz numbers
multi-point correlators

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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.",

keywords = "Jacobi ensemble, Hurwitz numbers, multi-point correlators",

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

year = "2021",

language = "English",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

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TY - JOUR

T1 - Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

AU - Grava, Tamara

AU - Ruzza, Giulio

AU - Gisonni, Massimo

PY - 2021

Y1 - 2021

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

M3 - Article (Academic Journal)

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -