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No directed fractal percolation in zero area

Lincoln Chayes·Robin Pemantle·Yuval Peres
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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.

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Lincoln Chayes, Robin Pemantle, Yuval Peres. 1997-01-23. No directed fractal percolation in zero area. https://doi.org/10.1007/bf02732437

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