论文标题
一维软随机几何图中孤立节点数量的分布
The Distribution of the Number of Isolated Nodes in the 1-Dimensional Soft Random Geometric Graph
论文作者
论文摘要
我们研究了软随机几何图中的孤立节点的数量，该图构成长度为l的圆环（线段[0，L]具有周期性边界条件），并且在两个节点之间存在边缘，其概率取决于它们之间的距离。不同的节点对之间的边缘是相互独立的。在适当的缩放制度中，我们表明，隔离节点的数量总变化为泊松随机变量。结果暗示着连接随机图的概率上的上限。
We study the number of isolated nodes in a soft random geometric graph whose vertices constitute a Poisson process on the torus of length L (the line segment [0,L] with periodic boundary conditions), and where an edge is present between two nodes with a probability which depends on the distance between them. Edges between distinct pairs of nodes are mutually independent. In a suitable scaling regime, we show that the number of isolated nodes converges in total variation to a Poisson random variable. The result implies an upper bound on the probability that the random graph is connected.
