Continuum Percolation with Unreliable and Spread-Out Connections
نویسندگان
چکیده
منابع مشابه
Continuum Percolation with Unreliable and Spread-Out Connections
We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models. Namely, when the selection mechanism according to which nodes are connected to each other, is sufficiently spread out, then a lower density of nodes, or on average fewer connections per node, are sufficient to obtain an unbounded connected component. We look...
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Fix d ≥ 2, and let X be either Z or the points of a Poisson process in R 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 [8], who showed that, as r → ∞, the average degree of the corresponding random graph at the percolation threshold tends...
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Fix d ≥ 2, and let X be either Z or the points of a Poisson process in R 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 [8], who showed that, as r →∞, the average degree of the corresponding random graph at the percolation threshold tends ...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2005
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-004-8826-0