Visible parts of fractal percolation

Details Visible parts of fractal percolation Visible parts of fractal percolation

2009-11-19

arxiv.org/abs/0911.3931v1

Mathematics

Classical Analysis and ODEs

22 pages, 3 figures

Scientific paper

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.

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