Visible parts of fractal percolation
Classical Analysis and ODEs
2013-03-25 v1 Probability
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.
Keywords
Cite
@article{arxiv.0911.3931,
title = {Visible parts of fractal percolation},
author = {I. Arhosalo and E. Järvenpää and M. Järvenpää and M. Rams and P. Shmerkin},
journal= {arXiv preprint arXiv:0911.3931},
year = {2013}
}
Comments
22 pages, 3 figures