标题： 非相交布朗运动的边界渐进行为：佩斯利、艾里和一个过渡 显示英文标题

标题： Boundary Asymptotics of Non-Intersecting Brownian Motions: Pearcey, Airy and a Transition

摘要： 我们研究$n$不相交的布朗运动，对应于$n\times n$厄米布朗运动的特征值。 在它们的极限形状边界处，我们发现只有三种普遍过程可能出现：在合并点附近的Pearcey过程，边缘处的Airy线集，以及一种新的确定性过程，用于描述从Pearcey过程到Airy线集的转变。 这三种情况由一个非常简单的积分条件区分。 我们的结果在非常温和的假设下成立，特别是我们不要求初始配置在$n\to\infty$时有任何类型的收敛性。 给出了对宏观和介观块的最大特征值以及随机初始配置的应用。 显示英文摘要

摘要： 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.