论文标题
通过短途编码的循环的汇合
Convergences of looptrees coded by excursions
论文作者
论文摘要
为了研究循环的融合，我们从实价Càdlàg函数中构造了连续树和循环，而无负跳跃称为偏移。然后，我们提供一个工具箱来通过游览来操纵两个产生的度量标准编码，并正式化跳跃对应于环路的原理，并且连续生长对应于分支。结合这些编码会从我们称之为白血病树的游览中创建新的度量空间。它们由沿树结构粘合的环和树木组成，使它们统一树木和循环。我们还提出了对绿色树的拓扑定义，该定义产生了我们认为是研究循环融合的合适空间。但是，这些第一个编码缺乏一些功能连续性，因此我们将其调整。因此，我们获得了几个限制定理。最后，我们提出了一些概率应用，例如证明了随机离散循环的不变性原则。
In order to study convergences of looptrees, we construct continuum trees and looptrees from real-valued càdlàg functions without negative jumps called excursions. We then provide a toolbox to manipulate the two resulting codings of metric spaces by excursions and we formalize the principle that jumps correspond to loops and that continuous growths correspond to branches. Combining these codings creates new metric spaces from excursions that we call vernation trees. They consist of a collection of loops and trees glued along a tree structure so that they unify trees and looptrees. We also propose a topological definition for vernation trees, which yields what we argue to be the right space to study convergences of looptrees. However, those first codings lack some functional continuity, so we adjust them. We thus obtain several limit theorems. Finally, we present some probabilistic applications, such as proving an invariance principle for random discrete looptrees.
