English

Forward clusters for degenerate random environments

Probability 2016-08-10 v1

Abstract

We consider connectivity properties and asymptotic slopes for certain random directed graphs on Z2Z^2 in which the set of points CoC_o that the origin connects to is always infinite. We obtain conditions under which the complement of CoC_o has no infinite connected component. Applying these results to one of the most interesting such models leads to an improved lower bound for the critical occupation probability for oriented site percolation on the triangular lattice in 2 dimensions.

Keywords

Cite

@article{arxiv.1307.2787,
  title  = {Forward clusters for degenerate random environments},
  author = {Mark Holmes and Thomas S. Salisbury},
  journal= {arXiv preprint arXiv:1307.2787},
  year   = {2016}
}
R2 v1 2026-06-22T00:48:59.220Z