A point process describing the component sizes in the critical window of the random graph evolution

Svante Janson, Joel Spencer

Research output: Contribution to journalArticlepeer-review

Abstract

We study a point process describing the asymptotic behaviour of sizes of the largest components of the random graph G(n,p) in the critical window, that is, for p = n-1 + λn-4/3, where A is a fixed real number. In particular, we show that this point process has a surprising rigidity. Fluctuations in the large values will be balanced by opposite fluctuations in the small values such that the sum of the values larger than a small ε (a scaled version of the number of vertices in components of size greater than εn2/3) is almost constant.

Original languageEnglish (US)
Pages (from-to)631-658
Number of pages28
JournalCombinatorics Probability and Computing
Volume16
Issue number4
DOIs
StatePublished - Jul 2007

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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