Packing densities and simulated tempering for hard core Gibbs point processes

Annals of the Institute of Statistical Mathematics

Volumn 53, Issue 4, 2001, Pages 661-680

  Mase, S ^a   MOller J ^b   Stoyan, D ^c   Waagepetersen, R P ^b   Doge G ^c  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b AALBORG UNIVERSITY   (Denmark)

^c TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

Closest packing density; Hard core Gibbs point processes; Intensity; Markov chain Monte Carlo; Metropolis Hastings; Phase transition; Simulated tempering; Spatial statistics; Statistical physics; Stochastic geometry

Indexed keywords

EID: 6644221561     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014662415827     Document Type: Article

References (41)

1. Alder, B. J. and Wainwright, T. E. (1957). Phase transition of a hard sphere system, Journal of Chemical Physics, 27, 1208-1209.
2. Alder, B. J. and Wainwright, T. E. (1962). Phase transition in elastic disks, Phys. Rev., 127, 359-361.
3. Allen, M. P. and Tildesley, D. J. (1987). Computer Simulation of Liquids, Oxford University Press, Oxford.
4. Bourbaki, N. (1958). Élements de Mathématique, Fonctions d'une variable réelle (Théorie Élémentaire), Hermann, Paris.
5. Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes, Springer, New York.
6. Diggle, P. J. (1983). Statistical Analysis of Spatial Point Patterns, Academic Press, London.
7. Ferguson, S. P. and Hales, T. C. (1998). A formulation of the Kepler conjecture (manuscript).
8. Fernández, J. F., Alonso, J. J. and Stankiewicz, E. (1995). One-stage continuous melting transition in two dimensions, Phys. Rev. Lett., 75, 3477-3480.
9. Georgii, H.-O. (1994). Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction, Probab. Theory Related Fields, 99, 171-195.
10. Georgii, H.-O. (1995). The equivalence of ensembles for classical systems of particles, J. Statist. Phys., 80, 1341-1378.
11. Georgii, H.-O. (2000). Phase transition and percolation in Gibbsian particle models, Statistical Phyisics and Spatial Statistics (eds. Klaus R. Mecke and Dietrich Stoyan), Springer Lecure Notes in Physics, 554, 267-294, Springer, Berlin.
12. Georgii, H.-O. and Häggström, O. (1996). Phase transition in continuum Potts models, Comm. Math. Phys., 181, 507-528.
13. Geyer, C. J. (1992). Practical Markov chain Monte Carlo (with discussion), Statist. Sci., 7, 473-511.
14. Geyer, C. J. (1999). Likelihood inference for spatial point processes, Stochastic Geometry: Likelihood and Computations (eds. O. E. Barndorff-Nielsen, W. S. Kendall and M. N. M. van Lieshout), 79-140, Chapman and Hall/CRC, London.
15. Geyer, C. J. and Møller, J. (1994). Simulation procedures and likelihood inference for spatial point processes, Scand. J. Statist., 21, 359-373.
16. Geyer, C. J. and Thompson, E. A. (1995). Annealing Markov chain Monte Carlo with applications to pedigree analysis, J. Amer. Statist. Assoc., 90, 909-920.
17. Hales, T. C. (1997a). Sphere packings I, Discrete Comput. Geom., 17, 1-51.
18. Hales, T. C. (1997b). Sphere packings II, Discrete Comput. Geom., 18, 135-149.
19. Hales, T. C. (1998a). Sphere packings III (manuscript).
20. Hales, T. C. (1998b). Sphere packings IV (manuscript).
21. Hales, T. C. (1998c). The Kepler conjecture (manuscript).
22. Hales, T. C. (1998d). An overview of the Kepler conjecture (manuscript).
23. Hansen, J.-P. and McDonald, I. R. (1986). Theory of Simple Liquids, Academic Press, London.
24. Hoover, W. G. and Ree, F. H. (1969). Melting transition and communal entropy for hard spheres, Journal of Chemical Physics, 49, 3609-3617.
25. Marinari, E. and Parisi, G. (1992). Simulated tempering: A new Monte Carlo scheme, Europhys. Lett., 19, 451-458.
26. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equation of state calculations by fast computing machines, Journal of Chemical Physics, 21, 1087-1092.
27. Meyn, S. P. and Tweedie, R. L. (1993). Markov Chains and Stochastic Stability, Springer, London.
28. Mitus, A. C., Weber, H. and Marx, D. (1997). Local structure analysis of the hard-disk fluid near melting, Phys. Rev. E, 55, 6855-6859.
29. Möller, J. (1999). Markov chain Monte Carlo and spatial point processes, Stochastic Geometry: Likelihood and Computations (eds. O. E. Barndorff-Nielsen, W. S. Kendall and M. N. M. van Lieshout), 141-172, Chapman and Hall/CRC, London.
30. Ripley, B. D. (1976). The second-order analysis of stationary point processes, J. Appl. Probab., 13, 255-266.
31. Ruelle, D. (1988). Statistical Mechanics: Rigorous Results, Addison-Wesley, Redwood City, California.
32. Salsburg, Z. W., Rudd, W. G. and Stillinger, F. H. (1967). Rigid disks at high density, II, Journal of Chemical Physics, 47, 4534-4539.
33. Sokal, A. D. (1997). Monte Carlo methods in statistical mechanics: Foundations and new algorithms, Functional integration (Cargèse, 1996), NATO Adv. Sci. Inst. Ser. B. Phys., 361, 131-192.
34. Stillinger, F. H., Salsburg, Z. W. and Kornegay, R. L. (1905). Rigid disks at high density, Journal of Chemical Physics, 43, 932-943.
35. Stoyan, D. and Schlather, M. (2000). Random sequential adsorption: Relation-ship to dead leaves and characterization of variability, J. Statist. Phys., 100, 969-979.
36. Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes and Point Fields, Wiley, Chichester.
37. Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and its Applications, 2nd ed., Wiley, New York.
38. Strandburg, K. J. (1988). Two-dimensional melting, Rev. Modern. Phys., 60, 161-207.
39. Tóth, L. F. (1972). Lagerungen in der Ebene, auf der Kugel und im Raum, Springer, Heidelberg.
40. Truskett, T. M., Torquato, S., Sastry, S., Debenetti, P. G. and Stillinger, F. H. (1998). A structural precursor to freezing in the hard-disk and hard-sphere systems, Phys. Rev. E, 58, 3083-3088.
41. Weber, H., Marx, D. and Binder, K. (1995). Melting transition in two dimensions: A finite-size analysis of bond-orientational order in hard disks, Phys. Rev. B, 51, 14636-14651.