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.

arXiv comment28 pages V3: section 3 revised

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Cited by in corpus (5)

• The classical $\beta$-ensembles with $\beta$ proportional to $1/N$: from loop equations to Dyson's disordered chain
• Relations between moments for the Jacobi and Cauchy random matrix ensembles
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
• Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method
• Symmetric Function Theory and Unitary Invariant Ensembles