Spread-out percolation in R^d

Let $X$ be either $Z^d$ or the points of a Poisson process in $R^d$ of intensity 1. Given parameters $r$ and $p$, join each pair of points of $X$ within distance $r$ independently with probability $p$. This is the simplest case of a `spread-out' percolation model studied by Penrose, who showed...

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Bibliographic Details
Main Authors: Bollobas, B, Janson, S, Riordan, O
Format: Journal article
Language:English
Published: 2005