26 citations · 107 across the 18 of their papers we have counts for
18 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 Lewański, 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 the…
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…
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. Th…
Jánossy densities and Darboux transformations for the Stark and cylindrical KdV equations
Tom Claeys, Gabriel Glesner, Giulio Ruzza +1
We study Jánossy densities of a randomly thinned Airy kernel determinantal point process. We prove that they can be expressed in terms of solutions to the Stark and cylindrical Kor…
Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process
Mattia Cafasso, Giulio Ruzza
We study the finite-temperature deformation of the discrete Bessel point process. We show that its largest particle distribution satisfies a reduction of the 2D Toda equation, as w…
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…
Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ
Christophe Charlier, Tom Claeys, Giulio Ruzza
We obtain uniform asymptotics for deformed Airy kernel determinants, which arise in models of finite temperature free fermions and which characterize the narrow wedge solution of t…
On the spectral problem of the quantum KdV hierarchy
Giulio Ruzza, Di Yang
The spectral problem for the quantum dispersionless Korteweg-de Vries (KdV) hierarchy, aka the quantum Hopf hierarchy, is solved by Dubrovin. In this article, following Dubrovin, w…
Higgs fields, non-abelian Cauchy kernels and the Goldman symplectic structure
Marco Bertola, Chaya Norton, Giulio Ruzza
We consider the moduli space of vector bundles of rank and degree over a fixed Riemann surface of genus . We use the explicit parametrization in terms of the Tyur…
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…
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…
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…
Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals
Massimo Gisonni, Tamara Grava, Giulio Ruzza
We consider the Laguerre partition function, and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn…
Brezin-Gross-Witten tau function and isomonodromic deformations
Marco Bertola, Giulio Ruzza
The Brezin-Gross-Witten tau function is a tau function of the KdV hierarchy which arises in the weak coupling phase of the Brezin-Gross-Witten model. It falls within the family of…
The Kontsevich-Penner matrix integral, isomonodromic tau functions and open intersection numbers
Marco Bertola, Giulio Ruzza
We identify the Kontsevich-Penner matrix integral, for finite size , with the isomonodromic tau function of a rational connection on the Riemann sphere with Fuch…