Percolation and first-passage percolation on oriented graphs
arXiv: Probability(2018)
摘要
We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices ^d that are translation-invariant and may contain loops. We exhibit some examples showing that the critical probability for the existence of an infinite cluster may be direction-dependent. Then, we prove that the phase transition in a given direction is sharp, and study the links between percolation and first-passage percolation on these oriented graphs.
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关键词
graphs,first-passage
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