The critical random graph, with martingales

Asaf Nachmias*, Yuval Peres

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

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
Volume176
Issue number1
DOIs
StatePublished - Mar 2010
Externally publishedYes

Funding

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

    Fingerprint

    Dive into the research topics of 'The critical random graph, with martingales'. Together they form a unique fingerprint.

    Cite this