%0 Journal Article %T The critical random graph, with martingales %A Asaf Nachmias %A Yuval Peres %J Mathematics %D 2005 %I arXiv %X 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. %U http://arxiv.org/abs/math/0512201v4