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Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction


 
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1. Title Title of document Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction
 
2. Creator Author's name, affiliation, country David Dereudre; Université de Valenciennes; France
 
2. Creator Author's name, affiliation, country Hans-Otto Georgii; LMU München; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Delaunay triangulation; Voronoi tessellation; Gibbs measure; variational principle; free energy; pressure; large deviations
 
3. Subject Subject classification 60K35; 60D05; 60G55; 82B21
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-11-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/713
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-713
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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