Arhosalo, I. and Järvenpää, E. and Järvenpää, M. and Rams, M. and Shmerkin, P. (2009) Visible parts of fractal percolation. [MIMS Preprint]
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Abstract
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | CICADA, fractal percolation, visible parts, Hausdorff dimension |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 28 Measure and integration MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes |
| Depositing User: | Mr Pablo Shmerkin |
| Date Deposited: | 27 Nov 2009 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1356 |
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