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 language | English |
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Article number | 49 |
Pages (from-to) | 1-8 |
Number of pages | 8 |
Journal | Electronic Communications in Probability |
Volume | 23 |
Issue number | 49 |
DOIs | |
Publication status | Published - 31 Jul 2018 |
Keywords
- Critical value
- Percolation
- Poisson process
- Vacant region
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty