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

Mathew Penrose

doi:10.1214/18-ECP153

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

Mathew Penrose

Research output: Contribution to journal › Article › peer-review

5 Citations (SciVal)

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
Article number	49
Pages (from-to)	1-8
Number of pages	8
Journal	Electronic Communications in Probability
Volume	23
Issue number	49
DOIs	https://doi.org/10.1214/18-ECP153
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

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10.1214/18-ECP153Licence: CC BY

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title = "Non-triviality of the vacancy phase transition for the Boolean model",

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.",

keywords = "Critical value, Percolation, Poisson process, Vacant region",

author = "Mathew Penrose",

year = "2018",

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AU - Penrose, Mathew

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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 - Critical value

KW - Percolation

KW - Poisson process

KW - Vacant region

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

UR - http://www.scopus.com/inward/record.url?scp=85052882900&partnerID=8YFLogxK

U2 - 10.1214/18-ECP153

DO - 10.1214/18-ECP153

M3 - Article

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VL - 23

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EP - 8

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

IS - 49

M1 - 49

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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