Abstract
The present stuffy deals with the existence of Delaunay pairwise Gibbs point process with superstable component by using the well-known Preston theorem. In particular, we prove the stability, the lower regularity, and the quasilocality properties of the Delaunay model.
Similar content being viewed by others
REFERENCES
A. Baddeley and J. Møller, Nearest-neighbour Markov point processes and random sets, Int. Statist. Rev. 57:89–121 (1989).
E. Bertin, J.-M. Billiot, and R. Drouilhet, Existence of “Nearest-Neighbour” Gibbs point models, Adv. Appl. Prob. 31(4) (1999). (To appear).
E. Bertin, J.-M. Billiot, and R. Drouilhet, Spatial Delaunay Gibbs point processes, Stochastic Models 15(2) (1999). (To appear).
R. Dobrushin, Gibbsian random field. The general case, Func. Anal. Appl. 3:22–28 (1969).
H.-O. Georgii, Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction, Probability Theory and Related Fields 99:171–195 (1994).
H.-O. Georgii and O. Häggström, Phase transition in continuum Potts models, Commun. Math. Phys. 181:507–528 (1996).
C. Geyer, Likelihood inference for spatial point processes, in Stochastic Geometry, Likelihood and Computation, O. E. Barndoff-Nielsen, W. S. Kendall, and M. N. M. van Lieshout, eds. (Chapman and Hall, London, 1998) (to appear).
C. Geyer and J. Møller, Simulation procedures and likelihood inference for spatial point processes, Scand. J. Statist. 21:359–373 (1994).
W. Greenberg, Thermodynamics states of classical systems, Commun. Math. Phys. 22:259–268 (1971).
C. Gruber and J. Lebowitz, Equilibrium states for classical systems, Commun. Math. Phys. 41:11–18 (1975).
D. Klein, Convergence of grand canonical Gibbs measures, Commun. Math. Phys. 92:295–308 (1984).
O. Lanford and D. Ruelle, Observables at infinity and states with support range correlations in statistical mechanics, Commun. Math. Phys. 13:194–215 (1969).
J. Møller, Lectures on random Voronoi tessellations, in Lecture Notes in Statistics, Vol. 87 (Springer-Verlag, New York, 1994).
F. Preparata and M. Shamos, Computational Geometry, an Introduction (Springer Verlag, New York, 1988).
C. Preston, Random Fields, Vol. 534 (Springer-Verlag, Berlin/Heidelberg/New York, 1976).
D. Ruelle, Statistical Mechanics (Benjamin, New York/Amsterdam, 1969).
D. Ruelle, Superstable interactions in classical statistical mechanics, Commun. Math. Phys. 18:127–159 (1970).
D. Stoyan, W. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, 2nd ed. (Wiley, Chichester, 1995).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bertin, E., Billiot, JM. & Drouilhet, R. Existence of Delaunay Pairwise Gibbs Point Process with Superstable Component. Journal of Statistical Physics 95, 719–744 (1999). https://doi.org/10.1023/A:1004551527790
Issue Date:
DOI: https://doi.org/10.1023/A:1004551527790