The critical random graph, with martingales

@article{Nachmias2005TheCR,
  title={The critical random graph, with martingales},
  author={A. Nachmias and Y. Peres},
  journal={Israel Journal of Mathematics},
  year={2005},
  volume={176},
  pages={29-41}
}
  • A. Nachmias, Y. Peres
  • Published 2005
  • Mathematics
  • Israel Journal of Mathematics
  • We give a short proof that the largest component C1 of the random graph G(n, 1/n) is of size approximately n2/3. The proof gives explicit bounds for the probability that the ratio is very large or very small. In particular, the probability that n−2/3|C1| exceeds A is at most $${e^{ - c{A^3}}}$$ for some c > 0. 
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