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A note on two-dimensional truncated long-range percolation
Published online by Cambridge University Press: 19 February 2016
Abstract
We prove that for a class of anisotropic long-range percolation models for which connection probabilities p<x,z> satisfy some regularity properties, and such that ∑z∈Z2p<x,z> = ∞, percolation still will occur even if we truncate all edges whose length exceeds some constant (which in this case depends on the family of connectivity probabilities {p<x,z>). We also present an example of dependent long-range percolation model for which this is not true.
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- General Applied Probability
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- Copyright © Applied Probability Trust 2001
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