Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T16:35:39.711Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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