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math-ph2020
Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
Massimo Gisonni, Tamara Grava, Giulio Ruzza
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…
math-ph2020
Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations
Mattia Cafasso, Tom Claeys, Giulio Ruzza
We study a family of unbounded solutions to the Korteweg-de Vries equation which can be constructed as log-derivatives of deformed Airy kernel Fredholm determinants, and which are…
math-ph2020
Matrix models for stationary Gromov-Witten invariants of the Riemann sphere
Marco Bertola, Giulio Ruzza
Inspired by recent formulæ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of as an isomonodromic tau fu…