The critical random graph, with martingales
Probability
2011-11-10 v4 Combinatorics
Abstract
We give a short proof that the largest component of the random graph is of size approximately . The proof gives explicit bounds for the probability that the ratio is very large or very small.
Cite
@article{arxiv.math/0512201,
title = {The critical random graph, with martingales},
author = {Asaf Nachmias and Yuval Peres},
journal= {arXiv preprint arXiv:math/0512201},
year = {2011}
}
Comments
13 pages, 1 figure. Revised version. Contains stronger probability deviation bounds and handles the entire scaling window. To appear in Israel Journal of Mathematics