### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Keywords

- Percolation
- Poisson process
- vacant region
- critical value

### Cite this

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

Research output: Contribution to journal › Article

*Electronic Communications in Probability*, vol. 23, no. 49, 49, pp. 1-8. https://doi.org/10.1214/18-ECP153

}

TY - JOUR

T1 - Non-triviality of the vacancy phase transition for the Boolean model

AU - Penrose, Mathew

PY - 2018/7/31

Y1 - 2018/7/31

N2 - 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.

AB - 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.

KW - Percolation

KW - Poisson process

KW - vacant region

KW - critical value

UR - https://arxiv.org/abs/1706.02197

U2 - 10.1214/18-ECP153

DO - 10.1214/18-ECP153

M3 - Article

VL - 23

SP - 1

EP - 8

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

IS - 49

M1 - 49

ER -