论文标题
在变化的边界下随机通风特征值的演变
Evolution of the Stochastic Airy eigenvalues under a changing boundary
论文作者
论文摘要
最初由Ramírez，Rider和Virág引入的通风$_β$点过程被定义为随机通风的操作员$ \ MATHCAL {H}_β$作用于$ l^2 [0，\ infty）$具有Dirichlet Boundary条件的子空间。在本文中，我们研究了定义为$ \ MATHCAL {H}_β$的特征值的耦合家族，其作用于$ l^2 [t，\ infty）$的子空间。这些点过程是通过$ \ mathcal {h}_β$的布朗术语结合的。我们表明，这些点过程作为$ t $的函数是可以通过显式计算的衍生产品来区分的。此外，当由$ t $延期时，结果点过程是固定的。此过程也可以被视为在三角形环境中对“ Gue Minor过程”的类似物。
The Airy$_β$ point process, originally introduced by Ramírez, Rider, and Virág, is defined as the spectrum of the stochastic Airy operator $\mathcal{H}_β$ acting on a subspace of $L^2[0,\infty)$ with Dirichlet boundary condition. In this paper we study the coupled family of point processes defined as the eigenvalues of $\mathcal{H}_β$ acting on a subspace of $L^2[t,\infty)$. These point processes are coupled through the Brownian term of $\mathcal{H}_β$. We show that these point processes as a function of $t$ are differentiable with explicitly computable derivative. Moreover when recentered by $t$ the resulting point process is stationary. This process can also be viewed as an analogue to the 'GUE minor process' in the tridiagonal setting.
