论文标题
装饰的稳定树
Decorated stable trees
论文作者
论文摘要
我们定义了装饰的$α$稳定的树木，这些树是通过将其分支点吹成随机的度量空间，从$α$稳定的树非正式地获得。这概括了Curien和Kortchemski的$α$稳定循环，这些度量空间只是确定性的圆圈。我们为这些对象提供不同的结构，这使我们能够理解它们的某些几何特性，包括紧凑性，Hausdorff维度和分布中的自相似性。我们证明了一个不变性原则，该原理指出，在某些条件下，类似的离散物体，随机装饰的离散树，将缩放限制收敛到装饰$α$稳定的树。我们提到了一些示例，其中这些对象出现在随机树和平面图的背景下，我们希望它们在更多情况下会自然出现。
We define decorated $α$-stable trees which are informally obtained from an $α$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $α$-stable looptrees of Curien and Kortchemski, where those metric spaces are just deterministic circles. We provide different constructions for these objects, which allows us to understand some of their geometric properties, including compactness, Hausdorff dimension and self-similarity in distribution. We prove an invariance principle which states that under some conditions, analogous discrete objects, random decorated discrete trees, converge in the scaling limit to decorated $α$-stable trees. We mention a few examples where those objects appear in the context of random trees and planar maps, and we expect them to naturally arise in many more cases.
