Journal of Statistical Physics

, Volume 58, Issue 5, pp 1109-1126

First online:

On the structure of Mandelbrot's percolation process and other random cantor sets

  • F. M. DekkingAffiliated withDelft University of Technology
  • , R. W. J. MeesterAffiliated withDelft University of Technology

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We consider generalizations of Mandelbrot's percolation process. For the process which we call the random Sierpinski carpet, we show that it passes through several different phases as its parameter increases from zero to one. The final section treats the percolation phase.

Key words

Percolation process random fractal set random substitution Hausdorff dimension