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Percolation in a Voronoi Competition-Growth Model

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Abstract

We study a model in which two entities (e.g., plant species, political ideas,...) compete for space on a plane, starting from randomly distributed seeds and growing deterministically at possibly different rates. An entity which forms an infinite cluster is considered to dominate over the other (which then cannot percolate). We analyze the occurrence of such a form of domination in situations in which one entity starts from a much larger density of seeds than the other one, but the latter one grows at a much faster rate than the former one. The model studied here generalizes the problem of Voronoi percolation.

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Authors and Affiliations

  1. Statistics Department, Universidade de São Paulo, Caixa Postal 66281, São Paulo, SP, 05315-970, Brazil;

    Elisabeti Kira & E. Jordão Neves

  2. Mathematics Department, UCLA, Los Angeles, California, 90095;

    Roberto H. Schonmann

Authors
  1. Elisabeti Kira
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  2. E. Jordão Neves
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  3. Roberto H. Schonmann
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Kira, E., Neves, E.J. & Schonmann, R.H. Percolation in a Voronoi Competition-Growth Model. Journal of Statistical Physics 92, 755–764 (1998). https://doi.org/10.1023/A:1023028207056

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  • DOI: https://doi.org/10.1023/A:1023028207056

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