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RESEARCH PRODUCT

Visible parts of fractal percolation

Ida ArhosaloPablo ShmerkinMichał RamsMaarit JärvenpääEsa Järvenpää

subject

28A80Plane (geometry)General MathematicsOpen problemProbability (math.PR)Mathematical analysisFractalDimension (vector space)Mathematics - Classical Analysis and ODEsPercolationHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsHausdorff measureAlmost surelyMathematics - ProbabilityMathematics

description

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.

yearjournalcountryeditionlanguage
2009-11-19
http://arxiv.org/abs/0911.3931