Continuum AB percolation and AB random geometric graphs

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3 Citations (Scopus)

Abstract

Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in d-space, with distance parameter r and intensities λ and μ. We show for d ≥ 2 that if λ is supercritical for the one-type random geometric graph with distance parameter 2r , there exists μ such that (λ, μ) is supercritical (this was previously known for d = 2). For d = 2, we also consider the restriction of this graph to points in the unit square. Taking μ = τ λ for fixed τ , we give a strong law of large numbers as λ → ∞ for the connectivity threshold of this graph.

Original languageEnglish
Pages (from-to)333-344
Number of pages12
JournalJournal of Applied Probability
Volume51A
DOIs
Publication statusPublished - 1 Dec 2014

Keywords

  • Bipartite geometric graph
  • Connectivity threshold
  • Continuum percolation

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