Speaker: Professor Dan Dai, City University of Hong Kong

Inviter: Xiangke Chang, Associate Professor

Title: Asymptotics of Fredholm determinant associated with the Pearcey kernel

Language: Chinese

Time & Venue: 2024.11.25 14:00-15:00 Tencent Meeting: 18501955795, Password: Amss@2473

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. 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.