Monday, March 11, 2013

1303.1871 (Thomas Bothner et al.)

Asymptotics of a cubic sine kernel determinant    [PDF]

Thomas Bothner, Alexander Its
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. Using the Riemann-Hilbert method, we calculate the large $s$-asymptotics of $\det(I-\gamma K_{\textnormal{csin}})$ for all values of the real parameter $\gamma$.
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