Percolation and first-passage percolation on oriented graphs
Abstract
We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices $\Z^d$ 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.
Domains
Probability [math.PR]Origin | Files produced by the author(s) |
---|