Advances in Applied Probability

Spatial STIT tessellations: distributional results for I-segments

Christoph Thäle, Viola Weiss, and Werner Nagel

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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.

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 3 (2012), 635-654.

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1346955258

Digital Object Identifier
doi:10.1239/aap/1346955258

Mathematical Reviews number (MathSciNet)
MR3024603

Zentralblatt MATH identifier
1262.60015

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 60E05: Distributions: general theory

Keywords
Cell division process iteration/nesting marked point process random tessellation stability under iteration stochastic geometry

Citation

Thäle, Christoph; Weiss, Viola; Nagel, Werner. Spatial STIT tessellations: distributional results for I-segments. Adv. in Appl. Probab. 44 (2012), no. 3, 635--654. doi:10.1239/aap/1346955258. https://projecteuclid.org/euclid.aap/1346955258


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