The critical random graph, with martingales

Details The critical random graph, with martingales The critical random graph, with martingales

2005-12-09

arxiv.org/abs/math/0512201v4

Mathematics

Probability

13 pages, 1 figure. Revised version. Contains stronger probability deviation bounds and handles the entire scaling window. To

Scientific paper

We give a short proof that the largest component of the random graph $G(n,
1/n)$ is of size approximately $n^{2/3}$. The proof gives explicit bounds for
the probability that the ratio is very large or very small.

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