Journal article
Forward Clusters for Degenerate Random Environments
M Holmes, TS Salisbury
Combinatorics Probability and Computing | CAMBRIDGE UNIV PRESS | Published : 2016
Abstract
We consider connectivity properties and asymptotic slopes for certain random directed graphs on ℤ2 in which the set of points that the origin connects to is always infinite. We obtain conditions under which the complement of 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 two dimensions.
Grants
Funding Acknowledgements
Holmes's research is supported in part by the Marsden fund, administered by RSNZ. Salisbury's research is supported in part by NSERC. Both authors acknowledge the hospitality of the Fields Institute, where part of this research was conducted. The authors sincerely wish to thank the referee, who completed a very thorough report. The referee's comments led to significant improvements in the paper.