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Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction

   
@article{EJP713,
	author = {David Dereudre and Hans-Otto Georgii},
	title = {Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {14},
	year = {2009},
	keywords = {Delaunay triangulation; Voronoi tessellation; Gibbs measure; variational principle; free energy; pressure; large deviations},
	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.},
	pages = {no. 85, 2438-2462},
	issn = {1083-6489},
	doi = {10.1214/EJP.v14-713},    
        url = {http://ejp.ejpecp.org/article/view/713}}