论文标题
稳定图：具有I.I.D的关键随机图的度量缩放限制。幂律学位
The stable graph: the metric space scaling limit of a critical random graph with i.i.d. power-law degrees
论文作者
论文摘要
我们证明，具有独立且分布的相同分布度的关键随机图具有指数尾部行为的指标缩放限制，其中$α+1 $，其中$α\ in（1,2）$。限制组件由随机$ \ mathbb {r} $ - 树木构建，该树由以上的游览超过其运行的过程，其法律与频谱正相关的$α$ stablelévy流程相对于本地定律绝对连续。这些跨越$ \ mathbb {r} $ - 树是测量$α$稳定的树。在每个这样的$ \ mathbb {r} $ - 树中，我们进行了一个随机数量的顶点身份，其位置由辅助泊松过程确定。这是在学位分布具有有限的第三刻（模型与ERDőS-rényi随机图中相同的通用类别的模型）以及$α$稳定的lévy过程的作用的情况下，这已经是已知的。
We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail behaviour with exponent $α+1$, where $α\in (1,2)$. The limiting components are constructed from random $\mathbb{R}$-trees encoded by the excursions above its running infimum of a process whose law is locally absolutely continuous with respect to that of a spectrally positive $α$-stable Lévy process. These spanning $\mathbb{R}$-trees are measure-changed $α$-stable trees. In each such $\mathbb{R}$-tree, we make a random number of vertex-identifications, whose locations are determined by an auxiliary Poisson process. This generalises results which were already known in the case where the degree distribution has a finite third moment (a model which lies in the same universality class as the Erdős--Rényi random graph) and where the role of the $α$-stable Lévy process is played by a Brownian motion.
