The asymptotic size of the largest component in random geometric graphs with some applications

Ge Chen, Chang-Long Yao, Tian-De Guo

Published 2013-11-05Version 1

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.