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The critical random graph, with martingales

Asaf Nachmias·Yuval Peres
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Abstract

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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Asaf Nachmias, Yuval Peres. 2005-12-09. The critical random graph, with martingales. https://arxiv.org/abs/math/0512201

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