On the integrable structure of deformed sine kernel determinants

Claeys, Tom;Tarricone, Sofia
(2024) Mathematical Physics, Analysis and Geometry — Vol. 27, n° 3 (2024)

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  • Claeys, Tomorcid-logoUCLouvain
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  • Tarricone, SofiaUCLouvain
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Abstract
We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We establish a connection between these determinants and a system of integro-differential equations generalizing the fifth Painlevé equation, and we show that they allow us to solve an integrable PDE explicitly for a large class of initial data.
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Claeys, T., & Tarricone, S. (2024). On the integrable structure of deformed sine kernel determinants. Mathematical Physics, Analysis and Geometry, 27(3). https://doi.org/10.1007/s11040-024-09476-x (Original work published 2024)