论文标题
与皮尔西内核相关的Fredholm决定因素的渐近学
Asymptotics of Fredholm determinant associated with the Pearcey kernel
论文作者
论文摘要
Pearcey内核是由随机矩阵理论引起的经典和通用的内核，它描述了特征值的局部统计数据，而限制的特征值则表现出尖尖的奇异性。它也出现在矩阵模型以外的各种统计物理模型中。我们考虑使用Pearcey内核在$ l^2 \ left（-s，s \右）$上作用的微量类类操作员的弗雷姆（Fredholm）决定因素。基于$ 3 \ times 3 $矩阵值的riemann-hilbert问题的最陡峭的下降分析，我们将弗雷德尔姆决定簇的渐近学作为$ s \ to +\ infty $，在随机矩阵理论的上下文中，这也被解释为大差距渐近差异。
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.
