Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
Massimo Gisonni, Tamara Grava, Giulio Ruzza
Abstract
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 formulæ 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.
Topics & Concepts
Unitary stateMathematicsUnitary matrixPure mathematicsInvariant (physics)Monotone polygonHurwitz matrixInterpretation (philosophy)Theta functionAlgebra over a fieldMatrix (chemical analysis)Generating functionOrthogonal polynomialsCombinatoricsWilson polynomialsSpecial unitary groupMinimal modelsAdvanced Combinatorial MathematicsMathematical functions and polynomialsQuantum Mechanics and Non-Hermitian Physics