Limit behaviors of random connected graphs driven by a Poisson process
Limit behaviors of random connected graphs driven by a Poisson process
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泊松过程驱动的随机连通图的限制行为
DOI：
10.1007/s11232-012-0085-7
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发表时间：
2012
影响因子：
1
通讯作者：
Y.Higuchi and C.H.Hu
中科院分区：
文献类型：
--
作者：
Z.H.Xu;Y.Higuchi and C.H.Hu
考虑一类具有随机顶点和随机边的随机连通图，其顶点随机分布由Poisson点过程给出，强度n局限于顶点，边的随机分布由连接函数给出。利用1992年欧几里得泛函上中心极限定理的Avram-Bertsimas方法，我们得到了中心极限定理过程的收敛速度、中等偏差以及依赖于随机连通图所有边的总长度的大偏差的一个上界。
We consider a class of random connected graphs with random vertices and random edges with the random distribution of vertices given by a Poisson point process with the intensity n localized at the vertices and the random distribution of the edges given by a connection function. Using the Avram-Bertsimas method constructed in1992for the central limit theorem on Euclidean functionals, we find the convergence rate of the central limit theorem process, the moderate deviation, and an upper bound for large deviations depending on the total length of all edges of the random connected graph.