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2009 Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction
David Dereudre, Hans-Otto Georgii
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Electron. J. Probab. 14: 2438-2462 (2009). DOI: 10.1214/EJP.v14-713


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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David Dereudre. Hans-Otto Georgii. "Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction." Electron. J. Probab. 14 2438 - 2462, 2009.


Accepted: 6 November 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60091
MathSciNet: MR2563247
Digital Object Identifier: 10.1214/EJP.v14-713

Primary: 60K35
Secondary: 60D05 , 60G55 , 82B21

Keywords: Delaunay triangulation , Free energy , Gibbs measure , large deviations , pressure , Variational principle , Voronoi tessellation

Vol.14 • 2009
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