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
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Authors Email ORCID Arhosalo, I UNSPECIFIED UNSPECIFIED Järvenpää, E UNSPECIFIED UNSPECIFIED Järvenpää, M UNSPECIFIED UNSPECIFIED Rams, M UNSPECIFIED UNSPECIFIED Shmerkin, P UNSPECIFIED UNSPECIFIED
Date :	1 June 2012
Identification Number :	https://doi.org/10.1017/S0013091509001680
Related URLs :	Author
Additional Information :	Copyright 2012 Cambridge University Press. Reprinted with permission.
Depositing User :	Symplectic Elements
Date Deposited :	28 Mar 2017 15:01
Last Modified :	28 Mar 2017 15:01
URI:	http://epubs.surrey.ac.uk/id/eprint/121092

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