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Boolean Percolation on Doubling Graphs

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 نشر من قبل Cristian Favio Coletti
 تاريخ النشر 2014
  مجال البحث
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We consider the discrete Boolean model of percolation on graphs satisfying a doubling metric condition. We study sufficient conditions on the distribution of the radii of balls placed at the points of a Bernoulli point process for the absence of percolation, provided that the retention parameter of the underlying point process is small enough. We exhibit three families of interesting graphs where the main result of this work holds. Finally, we give sufficient conditions for ergodicity of the discrete Boolean model of percolation.



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