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Line Segments in the Isotropic Planar Stit Tessellation

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  22 February 2016

Richard Cowan
Richard Cowan*
Affiliation:
University of Sydney
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: rcowan@usyd.edu.au
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Abstract

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This paper presents a powerful characterisation for the structure of internal vertices of the STIT's I-segments. The characterisation allows certain mathematical analyses to be performed easily. We demonstrate this by deriving new results for various topological properties of the tessellation: for example, the numbers of various types of edge and cell side within the typical I-segment. The characterisation also provides a tool for the calculations of metric properties of the tessellation; many new length distributions and frame-coverage results are given.

Keywords

Random tessellationSTIT tessellationstochastic 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 45 , Issue 2 , June 2013 , pp. 295 - 311
Copyright
© Applied Probability Trust 

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