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Existence of ‘nearest-neighbour’ spatial Gibbs models

Part of: Geometric probability and stochastic geometry Sufficiency and information

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

The present study deals with the existence of ‘nearest-neighbour’ type Gibbs models, introduced by Baddeley and Møller in 1989. In such models, the neighbourhood relation depends on the realization of the process. After giving new sufficient conditions to prove the existence of stationary Gibbs states, we deal with the first-nearest-neighbour model, the triplets Delaunay model, Ord's model and Markov connected component type models.

Keywords

Stochastic geometryGibbs point processesDelaunay triangulationnearest neighbour interactionDLR equationslocal specifications

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 31 , Issue 4 , December 1999 , pp. 895 - 909
Copyright
Copyright © Applied Probability Trust 1999 

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