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arXiv · 1508.05244

Fractal percolation, porosity, and dimension

Changhao Chen·Tuomo Ojala·Eino Rossi·Ville Suomala
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Abstract

We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less than $\tfrac12-\varepsilon$, or the lower porosity is larger than $\varepsilon$. Our method works also for inhomogeneous fractal percolation and more general random sets whose offspring distribution gives rise to a Galton-Watson process.

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Changhao Chen, Tuomo Ojala, Eino Rossi, Ville Suomala. 2015-08-21. Fractal percolation, porosity, and dimension. https://arxiv.org/abs/1508.05244

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