Visible parts of fractal percolation
Arhosalo, I, Järvenpää, E, Järvenpää, M, Rams, M and Shmerkin, P (2012) Visible parts of fractal percolation Proceedings of the Edinburgh Mathematical Society (Series 2), 55 (2). pp. 311-331.
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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: | Article | ||||||||||||||||||
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Divisions : | Faculty of Engineering and Physical Sciences > Mathematics | ||||||||||||||||||
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Date : | 1 June 2012 | ||||||||||||||||||
DOI : | 10.1017/S0013091509001680 | ||||||||||||||||||
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Additional Information : | Copyright 2012 Cambridge University Press. Reprinted with permission. | ||||||||||||||||||
Depositing User : | Symplectic Elements | ||||||||||||||||||
Date Deposited : | 28 Mar 2017 15:01 | ||||||||||||||||||
Last Modified : | 31 Oct 2017 14:19 | ||||||||||||||||||
URI: | http://epubs.surrey.ac.uk/id/eprint/121092 |
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