  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.
