No directed fractal percolation in zero area
Probability
2015-06-26 v1
Abstract
We show that fractal (or "Mandelbrot") percolation in two dimensions produces a set containing no directed paths, when the set produced has zero area. This improves a similar result by the first author in the case of constant retention probabilities to the case of retention probabilities approaching 1.
Keywords
Cite
@article{arxiv.math/9701222,
title = {No directed fractal percolation in zero area},
author = {Lincoln Chayes and Robin Pemantle and Yuval Peres},
journal= {arXiv preprint arXiv:math/9701222},
year = {2015}
}