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Spread-out percolation in R-d
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 31, no 2, 239-246 p.Article in journal (Refereed) Published
Abstract [en]

Fix d≥ 2, and let X be either ℤd or the points of a Poisson process in ℝd 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 [Ann Appl Probab 3 (1993) 253276], who showed that, as r, 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 [3] on inhomogeneous random graphs.

Place, publisher, year, edition, pages
2007. Vol. 31, no 2, 239-246 p.
Keyword [en]
Inhomogeneous, Percolation, Random graphs
National Category
URN: urn:nbn:se:uu:diva-12747DOI: 10.1002/rsa.20175ISI: 000248816600007OAI: oai:DiVA.org:uu-12747DiVA: diva2:40516
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2011-01-26Bibliographically approved

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Janson, Svante
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