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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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
|Deposited By:||Mr Pablo Shmerkin|
|Deposited On:||27 November 2009|