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2009.91: Visible parts of fractal percolation

2009.91: I. Arhosalo, E. Järvenpää, M. Järvenpää, M. Rams and P. Shmerkin (2009) Visible parts of fractal percolation.

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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 2000 > 28 Measure and integration
MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2009.91
Deposited By:Mr Pablo Shmerkin
Deposited On:27 November 2009

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