Asymptotics of a cubic sine kernel determinant

  title={Asymptotics of a cubic sine kernel determinant},
  author={Thomas Bothner and Alexander Its},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  • Thomas Bothner, A. Its
  • 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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