# Asymptotics of a cubic sine kernel determinant

@article{Bothner2013AsymptoticsOA,
title={Asymptotics of a cubic sine kernel determinant},
author={Thomas Bothner and Alexander Its},
journal={arXiv: Exactly Solvable and Integrable Systems},
year={2013}
}
• Published 8 March 2013
• Mathematics
• arXiv: Exactly Solvable and Integrable Systems
We study the one parameter family of Fredholm determinants $\det(I-\gamma K_{\textnormal{csin}}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{\textnormal{csin}}$ acting on the interval $(-s,s)$ whose kernel is a cubic generalization of the sine kernel which appears in random matrix theory. This Fredholm determinant appears in the description of the Fermi distribution of semiclassical non-equilibrium Fermi states in condensed matter physics as well as in random matrix theory…
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