Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds

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Abstract

We study competition of two spreading colors starting from single sources on the configuration model with i.i.d. degrees following a power-law distribution with exponent τ ∈ (2, 3). In this model two colors spread with a fixed but not necessarily equal speed on the unweighted random graph. We show that if the speeds are not equal, then the faster color paints almost all vertices, while the slower color can paint only a random subpolynomial fraction of the vertices. We investigate the case when the speeds are equal and typical distances in a follow-up paper.

Original languageEnglish
Article number116
Pages (from-to)1-48
Number of pages48
JournalElectronic Journal of Probability
Volume20
DOIs
Publication statusPublished - 4 Nov 2015

Keywords

  • Co-existence
  • Competition
  • Configuration model
  • Power law degrees
  • Random networks
  • Typical distances

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