Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process
Abstract
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 well as a discrete version of the integro-differential Painlev\'e II equation of Amir-Corwin-Quastel, and we compute initial conditions for the Poissonization parameter equal to 0. As proved by Betea and Bouttier, in a suitable continuum limit the last particle distribution converges to that of the finite-temperature Airy point process. We show that the reduction of the 2D Toda equation reduces to the Korteweg-de Vries equation, as well as the discrete integro-differential Painlev\'e II equation reduces to its continuous version. Our approach is based on the discrete analogue of Its-Izergin-Korepin-Slavnov theory of integrable operators developed by Borodin and Deift.
Keywords
Cite
@article{arxiv.2207.01421,
title = {Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process},
author = {Mattia Cafasso and Giulio Ruzza},
journal= {arXiv preprint arXiv:2207.01421},
year = {2023}
}
Comments
28 pages. V2: minor corrections