Asaf Nachmias, Yuval Peres
Published 2005-12-09, updated 2007-11-02Version 4
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.
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
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