One-Dimensional Geometric Random Graphs With Nonvanishing Densities—Part I: A Strong Zero-One Law for Connectivity
One-Dimensional Geometric Random Graphs With Nonvanishing Densities—Part I: A Strong Zero-One Law for Connectivity
复制标题
密度不为零的一维几何随机图 - 第一部分：强连通性零一定律
DOI：
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发表时间：
2009
影响因子：
2.5
通讯作者：
A. Makowski
中科院分区：
文献类型：
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作者：
Guang Han;A. Makowski
我们考虑一个由n个独立点组成的集合，这些点按照某个概率分布函数F分布在单位区间[0，1]上。如果两个节点的距离小于某个给定的阈值，则称它们相邻。当F具有非零密度f时，在弱连续性假设下证明了诱导几何随机图的连通性具有强的0 - 1律，并确定了相应的临界标度.这是通过推广到非均匀分布的一个极限结果得到的最大间距下的均匀分布的利维。
We consider a collection of n independent points which are distributed on the unit interval [0,1] according to some probability distribution function F. Two nodes are said to be adjacent if their distance is less than some given threshold value. When F admits a nonvanishing density f , we show under a weak continuity assumption on f that the property of graph connectivity for the induced geometric random graph exhibits a strong zero-one law, and we identify the corresponding critical scaling. This is achieved by generalizing to nonuniform distributions a limit result obtained by Levy for maximal spacings under the uniform distribution.