R-local Delaunay inhibition model

Journal of Statistical Physics

Volumn 132, Issue 4, 2008, Pages 649-667

  Bertin, Etienne ^a   Billiot, Jean Michel ^a   Drouilhet, Rémy ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

Correlation functions; D.L.R. equations; Delaunay triangulation; Inhibition property; Local specifications; Stationary Gibbs states

Indexed keywords

EID: 49249136842     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9565-4     Document Type: Article

References (15)

1. Baddeley, A.J., Møller, J.: Nearest-neighbour Markov point processes and random sets. Int. Stat. Rev. 57(2), 89-121 (1989)
2. Bertin, E., Billiot, J.-M., Drouilhet, R.: Existence of Delaunay pairwise Gibbs point processes with superstable component. J. Stat. Phys. 95, 719-744 (1999)
3. Bertin, E., Billiot, J.-M., Drouilhet, R.: Existence of "nearest-neighbour" Gibbs point models. Adv. Appl. Prob. 31, 895-909 (1999)
4. Bertin, E., Billiot, J.-M., Drouilhet, R.: Phase transition in nearest-neighbour continuum Potts models. J. Stat. Phys. 114(1/2), 79-100 (2004)
5. Connelly, R., Rybnikov, K., Volkov, S.: Percolation of the loss of tension in an infinite triangular lattice. J. Stat. Phys. 105(1/2), 143-171 (2001)
6. Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Springer Series in Statistics. Springer, New York (1988)
7. Georgii, H.-O.: Canonical and grand canonical Gibbs states for continuum systems. Commun. Math. Phys. 48, 31-51 (1976)
8. Georgii, H.-O., Häggström, O.: Phase transition in continuum Potts models. Commun. Math. Phys. 181, 507-528 (1996)
9. Georgii, H.-O., Zagrebnov, V.A.: On the interplay of magnetic and molecular forces in Curie-Weiss ferrofluid models. J. Stat. Phys. 93, 79-107 (1998)
10. Georgii, H.-O., Zessin, H.: Large deviations and the maximum entropy principle for marked point random fields. Probab. Theor. Relat. Fields 96, 177-204 (1993)
11. Kendall, W.S., van Lieshout, M.N.M., Baddeley, A.J.: Quermass-interaction processes: conditions for stability. Adv. Appl. Probab. 31, 315-342 (1999)
12. Menshikov, M., Rybnikov, K., Volkov, S.: The loss of tension in an infinite membrane with holes distributed according to a Poisson law. Adv. Appl. Probab. 34(2), 292-312 (2002)
13. Preston, C.J.: Random Fields, vol. 534. Springer, Berlin (1976)
14. Ruelle, D.: Statistical Mechanics. Benjamin, New York (1969)
15. Ruelle, D.: Superstable interactions in classical statistical mechanics. Commun. Math. Phys. 18, 127-159 (1970)