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- W2949277500 abstract "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 that, as $rtoinfty$, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the percolation threshold and the threshold for criticality of the naturally associated branching process approach one another. Here we show that this result follows immediately from of a general result of the authors on inhomogeneous random graphs." @default.
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- W2949277500 date "2007-01-01" @default.
- W2949277500 modified "2023-09-26" @default.
- W2949277500 title "Spread-out percolation inℝd" @default.
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- W2949277500 doi "https://doi.org/10.1002/rsa.20175" @default.
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