منابع مشابه
Spread-out percolation
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...
متن کاملSpread-out percolation in R
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 ...
متن کاملContinuum 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...
متن کاملThe survival probability for critical spread - out oriented percolation above 4 + 1 dimensions . II . Expansion
We derive a lace expansion for the survival probability for critical spread-out oriented percolation above 4+1 dimensions, i.e., the probability θn that the origin is connected to the hyperplane at time n, at the critical threshold pc. Our lace expansion leads to a nonlinear recursion relation for θn, with coefficients that we bound via diagrammatic estimates. This lace expansion is for point-t...
متن کاملConstruction of the incipient infinite cluster for spread-out oriented percolation above 4 + 1 dimensions
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on Zd × Z+, for d + 1 > 4 + 1. We consider two different constructions. For the first construction, we define Pn(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x, n) ∈ Z×Z+, summing this probability over x ∈ Zd, and normalisin...
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ژورنال
عنوان ژورنال: Random Structures and Algorithms
سال: 2007
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20175