Extreme paths in oriented 2D Percolation
Probability
2015-07-07 v2
Abstract
A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \cite{G} in the context of the contact process in continuous time. As discussed here, it also holds for several related models, including the discrete time contact process and two dimensional site percolation. Among the consequences are a natural monotonicity in the probability of percolation between different sites and a somewhat counter-intuitive correlation inequality.
Keywords
Cite
@article{arxiv.1411.0956,
title = {Extreme paths in oriented 2D Percolation},
author = {E. D. Andjel and L. F. Gray},
journal= {arXiv preprint arXiv:1411.0956},
year = {2015}
}