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arXiv · 2002.06370

Asymptotics of Fredholm determinant associated with the Pearcey kernel

Dan Dai·Shuai-Xia Xu·Lun Zhang
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Abstract

The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. We consider the Fredholm determinant of a trace class operator acting on $L^2\left(-s, s\right)$ with the Pearcey kernel. Based on a steepest descent analysis for a $3\times 3$ matrix-valued Riemann-Hilbert problem, we obtain asymptotics of the Fredholm determinant as $s\to +\infty$, which is also interpreted as large gap asymptotics in the context of random matrix theory.

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Dan Dai, Shuai-Xia Xu, Lun Zhang. 2020-02-15. Asymptotics of Fredholm determinant associated with the Pearcey kernel. https://doi.org/10.1007/s00220-021-03986-3

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