Abstract
We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices 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.
Funding Statement
ANR-16-CE40-0016
Citation
Olivier Garet. Régine Marchand. "Percolation and first-passage percolation on oriented graphs." Electron. Commun. Probab. 26 1 - 14, 2021. https://doi.org/10.1214/21-ECP419
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