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?



Collecting proofs of the birth of the giant component
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>


