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For the size of the largest component in a supercritical random geometricgraph, this paper estimates its expectation which tends to a polynomial on arate of exponential decay, and sharpens its asymptotic result with a centrallimit theory. Similar results can be obtained for the size of biggest opencluster, and for the number of open clusters of percolation on a box, and soon.

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