The Combinatorial Structure of Spatial STIT Tessellations

Autor(en): Thaele, Christoph
Weiss, Viola
Stichwörter: Combinatorial topology; Computer Science; Computer Science, Theory & Methods; Geometric mean values; Iteration/nesting; Mathematics; Random geometry; Random polytopes; Random tessellations; Stochastic geometry; Tilings
Erscheinungsdatum: 2013
Herausgeber: SPRINGER
Journal: DISCRETE & COMPUTATIONAL GEOMETRY
Volumen: 50
Ausgabe: 3
Startseite: 649
Seitenende: 672
Zusammenfassung: 
Spatially homogeneous random tessellations that are stable under iteration (nesting) in the -dimensional Euclidean space are considered, so-called STIT tessellations. They arise as outcome of a space-time process of subsequent cell division and, consequently, they are not facet-to-facet. The intent of this paper is to develop a detailed analysis of the combinatorial structure of such tessellations and to determine a number of new geometric mean values, for example for the neighbourhood of the typical vertex. The heart of the results is a fine classification of tessellation edges based on the type of their endpoints or on the equality relationship with other types of line segments. In the background of the proofs are delicate distributional properties of spatial STIT tessellations.
ISSN: 01795376
DOI: 10.1007/s00454-013-9524-y

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