2024年12月04日 星期三 登录 EN

学术活动
Asymptotics of Fredholm determinant associated with the Pearcey kernel
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报告人:
Dan Dai, Professor, City University of Hong Kong
邀请人:
Xiangke Chang, Associate Professor
题目:
Asymptotics of Fredholm determinant associated with the Pearcey kernel
时间地点:
14:00-15:00 November 25(Monday), Tencent Meeting: 650-568-120
摘要:

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.