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math.PROct 1, 2006
34
citations (OpenAlex)
authors
  • Asaf Nachmias
  • Yuval Peres
arXiv abstractPDF
paper

Component sizes of the random graph outside the scaling window

arXiv:math/0610466

Abstract

We provide simple proofs describing the behavior of the largest component of the Erdos-Renyi random graph G(n,p) outside of the scaling window, p={1+\eps(n) \over n} where \eps(n) tends to 0, but \eps(n)n^{1/3} tends to \infty.

13 pages

Cited by in corpus (11)

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  • Expansion of percolation critical points for Hamming graphs
  • Central limit theorem for statistics of subcritical configuration models
  • Bohman-Frieze processes at criticality and emergence of the giant component
  • A simple branching process approach to the phase transition in Gn,p​
  • Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs
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