Gibbs delaunay tessellations with geometric hardcore conditions

Journal of Statistical Physics

Volumn 131, Issue 1, 2008, Pages 127-151

  Dereudre, David ^a  

^a UNIVERSITÉ DE VALENCIENNES   (France)

Author keywords

Delaunay tessellation; Gibbs measure; Stochastic geometry

Indexed keywords

EID: 39749134713     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-007-9479-6     Document Type: Article

References (21)

1. Arak, T.: On Markovian random fields with finite number of values. In: 4th USSR-Japan Symposium on Probability Theory and Mathematical Statistics, Abstract of Communications, Tbilisi (1982)
2. Arak, T., Surgailis, D.: Markovian fields with polygonal realisations. Probab. Theory Relat. Fields 80, 543-579 (1989)
3. Arak, T., Surgailis, D.: Consistent polygonal fields. Probab. Theory Relat. Fields 89, 319-346 (1989)
4. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1999)
5. Bertin, E., Billiot, J.M., Drouilhet, R.: Spatial Delaunay Gibbs point process. Commun. Stat.-Stoch. Models 15(2), 181-199 (1999)
6. Bertin, E., Billiot, J.M., Drouilhet, R.: Existence of Delaunay pairwise Gibbs point process with superstable component. J. Stat. Phys. 95(3-4), 719-744 (1999)
7. Bertin, E., Billiot, J.M., Drouilhet, R.: Existence of nearest-neighbours spatial Gibbs models. Adv. Appl. Probab. (SGSA) 31, 895-909 (1999)
8. Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes, vol. I, 2nd edn. Springer, Berlin (2005)
9. Georgii, H.-O.: Canonical Gibbs Measures. Lecture Notes in Mathematics, vol. 760. Springer, Berlin (1979)
10. Glötzl, E.: Lokale Energien und Potentiale für Punktprozesse. Math. Nachr. 96, 195-206 (1980)
11. Matthes, K., Kerstan, J., Mecke, J.: Infinitely Divisible Point Process. Wiley, New York (1978)
12. Moller, J.: Random Tessellation. Wiley, New York (1978)
13. Nguyen, X.X., Zessin, H.: Integral and differential characterizations of the Gibbs process. Math. Nachr. 88, 105-115 (1979)
14. Preston, C.: Random Fields. Lecture Notes in Mathematics, vol. 714. Springer, Berlin (1976)
15. Ripley, B.: Modeling spatial patterns. J. R. Stat. Soc. B 39, 172-212 (1977)
16. Ruelle, D.: Statistical Mechanics. Rigorous Results. Benjamin, New York (1969)
17. Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. Math. Phys. 18, 127-159 (1970)
18. Schreiber, T.: Mixing properties of polygonal Markov fields in the plane. Preprint 18 of Faculty and Computer Science of the Nicolaus Copernicus University (2003)
19. Zahle, M.: Random cell complexes and generalised sets. Ann. Probab. 16, 1742-1766 (1966)
20. Zessin, H.: Lokale Energien und Potentiale für Punktprozesse. Math. Nachr. 96, 195-206 (1980)
21. Zessin, H.: Specific index and curvature for random simplicial complexes. Inst. Math. Natl. Acad. Sci. Armenia 37(1), 64-81 (2002)