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The set covariance of a dead leaves model

Part of: Multivariate analysis Global differential geometry Geometric probability and stochastic geometry

Published online by Cambridge University Press:  19 February 2016

Wilfried Gille
Wilfried Gille*
Affiliation:
Martin-Luther-Universität Halle-Wittenberg
*
∗ Postal address: Department of Physics, Martin-Luther-Universität Halle-Wittenberg, SAS-Laboratory, Hoher Weg 8, D-06120 Halle, Germany. Email address: [email protected]
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Abstract

The set covariance of a dead leaves model, constructed from hard spheres of constant diameter, is calculated analytically. The calculation is based on the covariance of a single sphere and on the pair correlation function of the centres of the spheres. There exist applications in the field of random sequential adsorption and in the interpretation of small-angle scattering experiments.

Keywords

Pair correlation functionset covarianceSAS-correlation function

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 62H35: Image analysis 53C80: Applications to physics
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 34 , Issue 1 , March 2002 , pp. 11 - 20
Copyright
Copyright © Applied Probability Trust 2002 

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References

Camko, C. G., Kulbac, A. A. and Maritschew, O. I. (1987). Integrali i proiswodnyje drobnowo porjadka i nekotoryje ich priloschenija. Integrale und Ableitungen Gebrochen-Rationaler Funktionen und einige Anwendungen. Nauka i Technika, Minsk (in Russian).Google Scholar
Feigin, L. A. and Svergun, D. I. (1987). Structure Analysis by Small-Angle X-Ray and Neutron Scattering. Plenum Press, New York.CrossRefGoogle Scholar
Gille, W. (1983). Stereologische Characterisierung von Mikroteilchensystemen mit der Röntgenkleinwinkelstreuung. , Martin-Luther-Universität Halle–Wittenberg.Google Scholar
Gille, W. (1995). Diameter distribution of spherical primary grains in the Boolean model from small-angle scattering. Part. Part. Syst. Charact. 12, 123–131.Google Scholar
Gille, W. (2000). Chord length distributions and small-angle scattering. Eur. J. Phys. B 17, 371–383.Google Scholar
Jeulin, D. (1997). Dead leaves models: from space tesselation to random functions. In Proc. Symp. Adv. Theory Appl. Random Sets (Fontainebleau, 9–11 October 1996), ed. Jeulin, D., World Scientific, River Edge, pp. 137–156.Google Scholar
Jeulin, D. (1998). Probabilistic models of structures. In Probamat 21st Century, ed. Frantziskonis, G. N. (NATO ASI Ser. 46), Kluwer, Dordrecht, pp. 233–257.Google Scholar
Matérn, B., (1960). Spatial variation. Meddelanden fran Statens Skogsforskningsinstitut 49, No. 5.Google Scholar
Matheron, G. (1968). Schéma booléen séquentiel de partition aléatoire. Res. Rep. N83, Centre de Morphologie Mathématique, École des Mines de Paris.Google Scholar
Matheron, G. (1975). Random Sets and Integral Geometry. John Wiley, New York.Google Scholar
Porod, G. (1951/52). Die Röntgenkleinwinkelstreuung von dichtgepackten kolloiden Systemen. Kolloid Z. 124, 83–114; 125, 51–122.Google Scholar
Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London.Google Scholar
Stoyan, D. and Schlather, M. (2000). Random sequential adsorption: relationship to dead leaves and characterization of variability. J. Statist. Phys. 100, 969–979.CrossRefGoogle Scholar
Stoyan, D., Kendall, W. S. and Mecke, J. (1987). Stochastic Geometry and Its Applications. Akademie Verlag, Berlin.Google Scholar