Abstract

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
Volume23
Issue number49
DOIs
Publication statusPublished - 31 Jul 2018

Fingerprint

Boolean Model
D-space
Vacancy
Poisson Model
Strictly positive
Poisson process
Euclidean
Ball
Union
Phase Transition
Radius
Moment
Poisson model
Phase transition

Keywords

  • Percolation
  • Poisson process
  • vacant region
  • critical value

Cite this

Non-triviality of the vacancy phase transition for the Boolean model. / Penrose, Mathew.

In: Electronic Communications in Probability, Vol. 23, No. 49, 49, 31.07.2018, p. 1-8.

Research output: Contribution to journalArticle

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