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The range of the mean-value quantities of planar tessellations

Published online by Cambridge University Press:  14 July 2016

Wilfrid S. Kendall  and
Joseph Mecke
Wilfrid S. Kendall*
Affiliation:
University of Strathclyde
Joseph Mecke*
Affiliation:
Friedrich-Schiller-Universität Jena
*
∗ Postal address: Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond St, Glasgow Gl 1XH, UK.
∗∗ Postal address: Department of Mathematics, Friedrich-Schiller-Universität Jena, DDR-6900 Jena, German Democratic Republic.
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Abstract

Many mean-value quantities of stationary random tessellations can be expressed in terms of three fundamental mean-value quantities. In this note we characterize the set of triples of mean values that can be realized, and show that every possible triple can arise from a suitable ergodic stationary isotropic tessellation.

Keywords

TESSELLATIONPOINT PROCESS INTENSITYRANDOM MEASURE INTENSITY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 411 - 421
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research carried out while this author was visiting the Department of Mathematics at the University of Strathclyde.

References

[1] Mecke, J. (1980) Palm methods for stationary random mosaics. In Combinatorial Principles in Stochastic Geometry, ed. Ambartzumian, R. V., Armenian Academy of Sciences, Erevan, 124–132.Google Scholar
[2] Mecke, J. (1984) Parametric representation of mean values for stationary random mosaics. Math. Operationsf. Statist. ser. Statist. 15, 437–442.Google Scholar
[3] Miles, R. E. (1961) Random Polytopes: The Generalisation to n Dimensions of the Intervals of a Poisson Process. , Cambridge University.Google Scholar
[4] Stoyan, D., Kendall, W. S. and Mecke, J. (1987) Stochastic Geometry and its Applications. Wiley, New York; Akademie-Verlag, Berlin.Google Scholar