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Title of Journal: J Stat Phys

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Abbravation: Journal of Statistical Physics

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Springer US

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DOI

10.1002/pssa.200778869

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1572-9613

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Emphasis Type="Italic"R/EmphasisLocal Delauna

Authors: Etienne Bertin JeanMichel Billiot Rémy Drouilhet
Publish Date: 2008/05/28
Volume: 132, Issue: 4, Pages: 649-
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Abstract

Unlike in the classical framework of Gibbs point processes usually acting on the complete graph in the context of nearestneighbour Gibbs point processes the nonnegativeness of the interaction functions do not ensure the local stability property This paper introduces domainwise but not pointwise inhibition stationary Gibbs models based on some tailormade Delaunay subgraphs All of them are subgraphs of the Rlocal Delaunay graph defined as the Delaunay subgraph specifically not containing the edges of Delaunay triangles with circumscribed circles of radii greater than some large positive real value R The usual relative compactness criterion for point processes needed for the existence result is directly derived from the Ruellebound of the correlation functions Furthermore assuming only the nonnegativeness of the energy function we have managed to prove the existence of the existence of Rlocal Delaunay stationary Gibbs states based on nonnegative interaction functions thanks to the use of the compactness of sublevel sets of the relative entropy

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