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Infinite clusters and critical values in two-dimensional circle percolation

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Abstract

We consider a dependent percolation model onZ 2 that does not have the ‘finite energy’ property. It is shown that the number of infinite clusters equals zero, one or infinity. Furthermore, we investigate a dynamical system which is associated with the calculation of the critical value in this model. It is shown that for almost all choices of the parameters in the model, this critical value can be calculated in a finite number of iterations.

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Authors and Affiliations

  1. Department of Mathematics, Delft University of Technology, Delft, The Netherlands

    Ronald W. J. Meester

  2. Department of Mathematics, Warsaw University, Warsaw, Poland

    Tomasz Nowicki

Authors
  1. Ronald W. J. Meester
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  2. Tomasz Nowicki
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Meester, R.W.J., Nowicki, T. Infinite clusters and critical values in two-dimensional circle percolation. Israel J. Math. 68, 63–81 (1989). https://doi.org/10.1007/BF02764969

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  • DOI: https://doi.org/10.1007/BF02764969

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