Asymptotics of Fredholm determinant associated with the Pearcey kernel (Q2662871)

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. The authors consider the Fredholm determinant of a trace class operator acting on \(L^2 (s,s)\) with the Pearcey kernel. Based on a steepest descent analysis for a \(3 \times 3\) matrix-valued Riemann-Hilbert problem, it is obtained asymptotics of the Fredholm determinant as \(s \rightarrow +\infty,\) which is also interpreted as large gap asymptotics in the context of random matrix theory.