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math-ph2024
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-ph2024
Jacobi Beta Ensemble and -Hurwitz Numbers
Giulio Ruzza
We express correlators of the Jacobi ensemble in terms of (a special case of) -Hurwitz numbers, a deformation of Hurwitz numbers recently introduced by Chapuy and Dolega. T…
math-ph2024
Quantum KdV hierarchy and quasimodular forms
Jan-Willem M. van Ittersum, Giulio Ruzza
Dubrovin has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg-de Vries (KdV) hierarchy is given by shifted s…