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I want to collect different proofs of Erdös-Rényi result on the double jump of the largest connected component on $G(n,p)$ (or in $G(n,M)$.

I know the original proof of Erdös-Rényi, the proof that uses Galton-Watson processes and the short proof of Sudakov and Krivelevich.

Are there other (essentially different) proofs of the result?

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Nachmias, Asaf, and Yuval Peres. "The critical random graph, with martingales." Israel Journal of Mathematics 176, no. 1 (2010): 29-41.

https://arxiv.org/abs/math/0512201

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