On the integrable structure of deformed sine kernel determinants
Mathematical Physics
2023-09-08 v1 Classical Analysis and ODEs
math.MP
Probability
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 Painlev\'e equation, and we show that they allow us to solve an integrable PDE explicitly for a large class of initial data.
Keywords
Cite
@article{arxiv.2309.03803,
title = {On the integrable structure of deformed sine kernel determinants},
author = {Tom Claeys and Sofia Tarricone},
journal= {arXiv preprint arXiv:2309.03803},
year = {2023}
}
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26 pages