University of Oulu

Chen, C., Ojala, T., Rossi, E. et al. J Theor Probab (2017) 30: 1471.

Fractal percolation, porosity, and dimension

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Author: Chen, Changhao1; Ojala, Tuomo2; Rossi, Eino2;
Organizations: 1Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland
2Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35 (MaD), 40014 University of Jyvaskyla, Finland
Format: article
Version: submitted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Springer Nature, 2017
Publish Date: 2017-11-28


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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Series: Journal of theoretical probability
ISSN: 0894-9840
ISSN-E: 1572-9230
ISSN-L: 0894-9840
Volume: 30
Issue: 4
Pages: 1471 - 1498
DOI: 10.1007/s10959-016-0680-x
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: CC and ER acknowledge the support of the Vilho, Yrjö, and Kalle Väisälä foundation. CC and VS acknowledge support from the Centre of Excellence in Analysis and Dynamics Research funded by the Academy of Finland
Copyright information: © 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: