论文标题
硬边缘过程的差距概率
Gap probability for the hard edge Pearcey process
论文作者
论文摘要
硬边缘皮尔西过程在随机矩阵理论和许多其他随机模型中是通用的。本文通过处理相关的弗雷霍尔姆决定因素，涉及间隔$（0，s）$上稀薄/未命中的硬边缘过程的差距概率。我们通过与哈密顿相关的耦合微分方程系统建立了差距概率的整体表示。加上对哈密顿量的一些显着的差异身份，我们得出了较大的差异渐近性，直至和包括恒定项。作为一种应用，我们还获得了硬边缘过程的计数函数的渐近统计特性。
The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval $(0,s)$ by working on the relevant Fredholm determinants. We establish an integral representation of the gap probability via a Hamiltonian related a system of coupled differential equations. Together with some remarkable differential identities for the Hamiltonian, we derive the large gap asymptotics for the thinned case, up to and including the constant term. As an application, we also obtain the asymptotic statistical properties of the counting function for the hard edge Pearcey process.
