Percolation and first-passage percolation on oriented graphs
Probability
2021-06-09 v2
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.
Cite
@article{arxiv.1807.05736,
title = {Percolation and first-passage percolation on oriented graphs},
author = {Olivier Garet and Régine Marchand},
journal= {arXiv preprint arXiv:1807.05736},
year = {2021}
}