The critical random graph, with martingales

Asaf Nachmias*, Yuval Peres

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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{pipe}C1{pipe} exceeds A is at most e-cA^3 for some c > 0.

Original languageEnglish
Pages (from-to)29-41
Number of pages13
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Mar 2010
Externally publishedYes


FundersFunder number
National Science Foundation
Directorate for Mathematical and Physical Sciences0104073, 0244479


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