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. In this talk, we consider the Fredholm determinant $/det/left(I-/gamma K^{/mathrm{Pe}}_{s,/rho}/right)$, where $0 /leq /gamma /leq 1$ and $K^{/mathrm{Pe}}_{s,/rho}$ stands for the trace class operator acting on $L^2/left(-s, s/right)$ with the classical 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.

This is a joint work with Shuai-Xia Xu and Lun Zhang.

海报