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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