English

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}
}