论文标题
非相反的布朗尼动议的边界渐近学：皮尔西，通风和过渡
Boundary Asymptotics of Non-Intersecting Brownian Motions: Pearcey, Airy and a Transition
论文作者
论文摘要
我们研究了$ n $ notchect的布朗尼动议，对应于$ n \ times n $ hermitian布朗尼运动的特征值。在其极限形状的边界上，我们发现只能出现三个通用过程：珍珠过程接近合并点，边缘的通风线集合以及一个新颖的确定过程，描述了从Pearcey过程到通风线集合的过渡。这三种情况以非常简单的整体条件而区分。我们的结果在非常温和的假设下成立，特别是我们不需要将初始配置作为$ n \ to \ infty $的任何类型的收敛性。给出了宏观和介质大容量的最大特征值以及随机初始配置的应用。
We study $n$ non-intersecting Brownian motions, corresponding to the eigenvalues of an $n\times n$ Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process close to merging points, the Airy line ensemble at edges and a novel determinantal process describing the transition from the Pearcey process to the Airy line ensemble. The three cases are distinguished by a remarkably simple integral condition. Our results hold under very mild assumptions, in particular we do not require any kind of convergence of the initial configuration as $n\to\infty$. Applications to largest eigenvalues of macro- and mesoscopic bulks and to random initial configurations are given.
