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Continuum percolation in the Gabriel graph

Part of: Sufficiency and information Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Etienne Bertin ,
Jean-Michel Billiot  and
Rémy Drouilhet
Etienne Bertin*
Affiliation:
Université Pierre Mendès France
Jean-Michel Billiot*
Affiliation:
Université Pierre Mendès France
Rémy Drouilhet*
Affiliation:
Université Pierre Mendès France
*
∗ Postal address: Labsad, BSHM, Université Pierre Mendès France, 1251 avenue centrale, BP 47, 38040 Grenoble Cedex 9, France.
∗ Postal address: Labsad, BSHM, Université Pierre Mendès France, 1251 avenue centrale, BP 47, 38040 Grenoble Cedex 9, France.
∗ Postal address: Labsad, BSHM, Université Pierre Mendès France, 1251 avenue centrale, BP 47, 38040 Grenoble Cedex 9, France.
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Abstract

In the present study, we establish the existence of site percolation in the Gabriel graph for Poisson and hard-core stationary point processes.

Keywords

PercolationGabriel graphhard-core point processPoisson point process

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 62B05: Sufficient statistics and fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 34 , Issue 4 , December 2002 , pp. 689 - 701
Copyright
Copyright © Applied Probability Trust 2002 

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