Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction

David Dereudre (Université de Valenciennes)
Hans-Otto Georgii (LMU München)

Abstract


This paper deals with stationary Gibbsian point processes on the plane with an interaction that depends on the tiles of the Delaunay triangulation of points via a bounded triangle potential. It is shown that the class of these Gibbs processes includes all minimisers of the associated free energy density and is therefore nonempty. Conversely, each such Gibbs process minimises the free energy density, provided the potential satisfies a weak long-range assumption.

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Pages: 2438-2462

Publication Date: November 6, 2009

DOI: 10.1214/EJP.v14-713

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