Spatial Stit Tessellations: Distributional Results for I-Segments
2012 ◽
Vol 44
(03)
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pp. 635-654
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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.
2012 ◽
Vol 44
(3)
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pp. 635-654
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Keyword(s):
1988 ◽
Vol 46
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pp. 26-27
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1991 ◽
Vol 115
(5)
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pp. 1267-1274
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2016 ◽
Vol 19
(1)
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pp. 101-114
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Keyword(s):
2011 ◽
Vol 17
(8)
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pp. 2113-2130
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