No directed fractal percolation in zero area

Details No directed fractal percolation in zero area No directed fractal percolation in zero area

1997-01-23

arxiv.org/abs/math/9701222v1

Mathematics

Probability

Scientific paper

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.

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