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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,μ. For any λ>0 we consider the percolation threshold μc(λ) associated to the parameter μ. Denoting by λc the percolation threshold for the standard Poisson Boolean model with radii r, we show the lower bound μc(λ)≥clog(c/(λ-λc)) for any λ>λc with c>0 a fixed constant. In particular, there is no phase transition in μ at the critical value of λ, that is, μc(λc) =∞.
Original languageEnglish
Pages (from-to)1228-1237
JournalJournal of Applied Probability
DOIs
Publication statusPublished - 1 Dec 2018

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