Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
Mathematical Physics
2022-07-27 v3 Classical Analysis and ODEs
Combinatorics
math.MP
Probability
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.
Cite
@article{arxiv.2011.04082,
title = {Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials},
author = {Massimo Gisonni and Tamara Grava and Giulio Ruzza},
journal= {arXiv preprint arXiv:2011.04082},
year = {2022}
}
Comments
28 pages V3: section 3 revised