Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

TL;DR

This paper links the topological expansion of the Jacobi Unitary Ensemble to triple monotone Hurwitz numbers and provides formulas for multipoint correlators using Wilson polynomials, advancing combinatorial and analytical understanding.

Contribution

It offers a new combinatorial interpretation of the topological expansion and generalizes formulas for multipoint correlators in the Jacobi Unitary Ensemble.

Findings

Topological expansion expressed via triple monotone Hurwitz numbers.

Effective formulas for multipoint correlators using Wilson polynomials.

Completes the combinatorial interpretation of classical unitary invariant ensembles.

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.