Visible parts of fractal percolation

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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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

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