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A lower bound on the box-counting dimension of crossings in fractal percolation

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  • Orzechowski, M. E.

Abstract

We consider Mandelbrot's fractal percolation process, obtained by repeated subdivision of the unit square, and obtain an explicit almost sure lower bound on the lower box-counting dimension of paths within the retained set that cross the square from left to right.

Suggested Citation

  • Orzechowski, M. E., 1998. "A lower bound on the box-counting dimension of crossings in fractal percolation," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 53-65, May.
    • Handle: RePEc:eee:spapps:v:74:y:1998:i:1:p:53-65
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    References listed on IDEAS

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    1. Chayes, L., 1996. "On the length of the shortest crossing in the super-critical phase of Mandelbrot's percolation process," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 25-43, January.
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