The asymptotic size of the largest component in random geometric graphs with some applications
Probability
2013-11-06 v1
Abstract
For the size of the largest component in a supercritical random geometric graph, this paper estimates its expectation which tends to a polynomial on a rate of exponential decay, and sharpens its asymptotic result with a central limit theory. Similar results can be obtained for the size of biggest open cluster, and for the number of open clusters of percolation on a box, and so on.
Keywords
Cite
@article{arxiv.1311.0984,
title = {The asymptotic size of the largest component in random geometric graphs with some applications},
author = {Ge Chen and Chang-Long Yao and Tian-De Guo},
journal= {arXiv preprint arXiv:1311.0984},
year = {2013}
}
Comments
22 pages, 2 figures