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Interdependences of directional quantities of planar tessellations

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Viola Weiss  and
Werner Nagel
Viola Weiss*
Affiliation:
Friedrich-Schiller-Universität Jena
Werner Nagel*
Affiliation:
Friedrich-Schiller-Universität Jena
*
∗ Postal address: Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, D-07740 Jena, Germany.
∗ Postal address: Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, D-07740 Jena, Germany.
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Abstract

For random planar stationary tessellations a parameter system of three mean values and two directional distributions of the edges is considered. To investigate the interdependences between these parameters their joint range is described, i.e. the set of values which can be realized by tessellations. The constructive proof is based on mixtures of stationary regular tessellations. To explore the range for the class of stationary ergodic tessellations a procedure is used which we refer to as iteration.

Keywords

Random tessellationergodicitydirectional distributiontessellation characteristicsmixtureiteration of tessellationsstochastic geometry

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 3 , September 1999 , pp. 664 - 678
Copyright
Copyright © Applied Probability Trust 1999 

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