SPATIAL STIT TESSELLATIONS: DISTRIBUTIONAL RESULTS FOR I-SEGMENTS

Autor(en): Thaele, Christoph
Weiss, Viola
Nagel, Werner
Stichwörter: 2ND-ORDER PROPERTIES; Cell division process; iteration/nesting; marked point process; Mathematics; NODES; random tessellation; SHAPES; stability under iteration; Statistics & Probability; stochastic geometry
Erscheinungsdatum: 2012
Herausgeber: APPLIED PROBABILITY TRUST
Journal: ADVANCES IN APPLIED PROBABILITY
Volumen: 44
Ausgabe: 3
Startseite: 635
Seitenende: 654
Zusammenfassung: 
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 1-segment. In preparation for its proof, we obtain other distributional identities for the typical 1-segment and the length-weighted typical I-segment, which provide new insight into the spatiotemporal construction process.
ISSN: 00018678

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