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arXiv · 2207.01421

Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process

Mattia Cafasso·Giulio Ruzza
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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.

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Mattia Cafasso, Giulio Ruzza. 2022-07-04. Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process. https://doi.org/10.1112/jlms.12745

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