The concepts of void and cluster for an arbitrary point distribution in a domain 𝒟 are defined and characterized by some parameters such as volume, density, number of points belonging to them, shape, etc. After assigning a weight to each void and cluster—which is a function of its characteristics—the concept of distance between two point configurations S1 and S2 in 𝒟 is introduced, both with and without the help of a lattice in the domain 𝒟. This defines a topology for the point distributions in 𝒟, which is different for the different characterizations of the voids and clusters.
REFERENCES
1.
M. S. Bartlett, The Statistical Analysis of Spatial Pattern (Chapman and Hall, London, 1975);
A. D. Cliff and J. K. Ord, Spatial Processes: Models and Applications (Pion, London, 1981);
D. R. Cox and V. Isham, Point Processes (Chapman and Hall, London, 1980);
P. J. Diggle, Statistical Analysis of Spatial Point Patterns (Academic, London, 1983);
B. D. Ripley, Spatial Statistics (Wiley, New York, 1981);
A. Rogers, Statistical Analysis of Spatial Dispersion (Pion, London, 1974).
2.
V.
de Lapparent
, M. J.
Geller
, and J. P.
Huchra
, Astrophys. J. Lett.
302
, L1
(1986
).3.
R. P.
Kirshner
, A.
Oemler
, Jr., P. L.
Schechter
, and S. A.
Schectman
, Astrophys. J. Lett.
248
, L57
(1981
).4.
F. R.
Bouchet
and M.
Lachièze‐Rey
, Astrophys. J. Lett.
302
, L37
(1986
);S.
Otto
, H. D.
Politzer
, and M. B.
Wise
, Phys. Rev. Lett.
56
, 1878
(1986
);H. D.
Politzer
and J. P.
Preskill
, Phys. Rev. Lett.
56
, 99
(1986
); , Phys. Rev. Lett.
S.
Otto
, H. D.
Politzer
, J.
Preskill
, and M. B.
Wise
, Astrophys. J.
304
, 62
(1986
).
This content is only available via PDF.
© 1987 American Institute of Physics.
1987
American Institute of Physics
You do not currently have access to this content.
