Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 44, Number 3 (2012), 635-654.
Spatial STIT tessellations: distributional results for I-segments
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.
Adv. in Appl. Probab., Volume 44, Number 3 (2012), 635-654.
First available in Project Euclid: 6 September 2012
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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