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Spread-out percolation in R^d

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 $r\to\infty$, 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 as...

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Publication status:
Published

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Publisher copy:
10.1002/rsa.20175
Journal:
Random Struct. Algorithms 31 (2007), 239-246. More from this journal
Volume:
31
Issue:
2
Pages:
239-246
Publication date:
2005-08-23
DOI:
EISSN:
1098-2418
ISSN:
1042-9832
Language:
English
Keywords:
Pubs id:
pubs:23582
UUID:
uuid:fa896c82-1a0e-4abc-bbc0-8284d0a27674
Local pid:
pubs:23582
Source identifiers:
23582
Deposit date:
2012-12-19

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