0000000000867624

AUTHOR

Ida Arhosalo

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Visible parts of fractal percolation

2009

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.

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
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