6 papers
ODE/IM Correspondence at the Free-Fermion Point. Laguerre Wronskians, Shifted Symmetric Functions, and Quantum KdV
Davide Masoero, Giulio Ruzza
We consider the ODE/IM correspondence for the value of the Virasoro central charge (free-fermion point) and the associated quantum KdV model the quantization of the seco…
On the large genus of Hurwitz numbers
Davide Accadia, Danilo LewaÅski, Giulio Ruzza
Hurwitz theory provides a large variety of enumerative problems related to algebraic geometry, mathematical physics, and combinatorics. We give a general framework to approach the…
Multiplicative Averages of Plancherel Random Partitions: Elliptic Functions, Phase Transitions, and Applications
Mattia Cafasso, Matteo Mucciconi, Giulio Ruzza
We consider random integer partitions that follow the Poissonized Plancherel measure of parameter . Using RiemannHilbert techniques, we establish the asymptotics of th…
Quantum KdV hierarchy and shifted symmetric functions
Jan-Willem van Ittersum, Giulio Ruzza
We study spectral properties of the quantum Korteweg-de Vries hierarchy defined by Buryak and Rossi. We prove that eigenvalues to first order in the dispersion parameter are given…
Bessel kernel determinants and integrable equations
Giulio Ruzza
We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics a…
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…