Geodesic
Limit behaviors of random connected graphs driven by a~Poisson process
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 28-39

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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 in 1992 for 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.
Keywords: random connected graph, dependency graph, central limit theorem, moderate deviation, large deviation. 
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     author = {Zhonghao Xu and Yasunari Higuchi and Chunhua Hu},
     title = {Limit behaviors of random connected graphs driven by {a~Poisson} process},
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Zhonghao Xu; Yasunari Higuchi; Chunhua Hu. Limit behaviors of random connected graphs driven by a~Poisson process. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 1, pp. 28-39. http://geodesic.mathdoc.fr/item/TMF_2012_172_1_a2/