Non-triviality of the vacancy phase transition for the Boolean model

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4 Citations (SciVal)


In the spherical Poisson Boolean model, one takes the union of random balls centred on the points of a Poisson process in Euclidean d-space with d >= 2. We prove that whenever the radius distribution has a finite d-th moment, there exists a strictly positive value for the intensity such that the vacant region percolates.
Original languageEnglish
Article number49
Pages (from-to)1-8
Number of pages8
JournalElectronic Communications in Probability
Issue number49
Publication statusPublished - 31 Jul 2018


  • Critical value
  • Percolation
  • Poisson process
  • Vacant region

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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