论文标题
热力学状态中的随机连接模型：添加成本稳定功能的中心极限定理
Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals
论文作者
论文摘要
本文处理一个随机连接模型，一个随机图，其顶点是由$ \ mathbb {r}^d $上的同质泊松点进程给出的，并且边缘是独立绘制的，这取决于两个端点的位置。我们在最小的假设下为该图上的一般功能建立了中央限制定理（CLT），这些假设是弱稳定的组合，而$（2+δ）$ - 时刻条件。结果，同构子图计数，同构成分计数，然后得出连接组件的数量。此外，还首次证明了Betti数字和最大组件大小的CLT。
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end points. We establish central limit theorems (CLT) for general functionals on this graph under minimal assumptions that are a combination of the weak stabilization for the-one cost and a $(2+δ)$-moment condition. As a consequence, CLTs for isomorphic subgraph counts, isomorphic component counts, the number of connected components are then derived. In addition, CLTs for Betti numbers and the size of biggest component are also proved for the first time.
