Fractal percolation, porosity, and dimension
Chen, Changhao; Ojala, Tuomo; Rossi, Eino; Suomala, Ville (2016-04-28)
Chen, C., Ojala, T., Rossi, E. et al. J Theor Probab (2017) 30: 1471. https://doi.org/10.1007/s10959-016-0680-x
© Springer Science+Business Media New York 2016. This is a pre-print of an article published in Journal of Theoretical Probability. The final authenticated version is available online at: https://doi.org/10.1007/s10959-016-0680-x
We study the porosity properties of fractal percolation sets E ⊂ Rd. Among other things, for all 0 < ɛ < ½, we obtain dimension bounds for the set of exceptional points where the upper porosity of E is less than ½ ‒ ɛ, or the lower porosity is larger than ɛ. 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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