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math-ph2025
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…
math-ph2025
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…