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.
Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials / Gisonni, M.; Grava, T.; Ruzza, G.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 111:3(2021), pp. 1-38. [10.1007/s11005-021-01396-z]
Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
Gisonni, M.;Grava, T.
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2021-01-01
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.| File | Dimensione | Formato | |
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