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September 2012 Spatial STIT tessellations: distributional results for I-segments
Christoph Thäle, Viola Weiss, Werner Nagel
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Adv. in Appl. Probab. 44(3): 635-654 (September 2012). DOI: 10.1239/aap/1346955258

Abstract

In this paper we consider three-dimensional random tessellations that are stable under iteration (STIT tessellations). STIT tessellations arise as a result of subsequent cell division, which implies that their cells are not face-to-face. The edges of the cell-dividing polygons are the so-called I-segments of the tessellation. The main result is an explicit formula for the distribution of the number of vertices in the relative interior of the typical I-segment. In preparation for its proof, we obtain other distributional identities for the typical I-segment and the length-weighted typical I-segment, which provide new insight into the spatiotemporal construction process.

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Christoph Thäle. Viola Weiss. Werner Nagel. "Spatial STIT tessellations: distributional results for I-segments." Adv. in Appl. Probab. 44 (3) 635 - 654, September 2012. https://doi.org/10.1239/aap/1346955258

Information

Published: September 2012
First available in Project Euclid: 6 September 2012

zbMATH: 1262.60015
MathSciNet: MR3024603
Digital Object Identifier: 10.1239/aap/1346955258

Subjects:
Primary: 60D05
Secondary: 60E05 , 60G55

Keywords: Cell division process , iteration/nesting , marked point process , random tessellation , stability under iteration , Stochastic geometry

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 3 • September 2012
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