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Consistency of constructions for cell division processes

Part of: Geometric probability and stochastic geometry Markov processes

Published online by Cambridge University Press:  21 March 2016

Werner Nagel  and
Eike Biehler
Werner Nagel*
Affiliation:
Friedrich-Schiller-Universität Jena
Eike Biehler*
Affiliation:
Friedrich-Schiller-Universität Jena
*
∗ Postal address: Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07737 Jena, Germany.
∗ Postal address: Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, D-07737 Jena, Germany.
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Abstract

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For a class of cell division processes in the Euclidean space ℝd, spatial consistency is investigated. This addresses the problem whether the distribution of the generated structures, restricted to a bounded set V, depends on the choice of a larger region W ⊃ V where the construction of the cell division process is performed. This can also be understood as the problem of boundary effects in the cell division procedure. It is known that the STIT tessellations are spatially consistent. In the present paper it is shown that, within a reasonable wide class of cell division processes, the STIT tessellations are the only ones that are consistent.

Keywords

Stochastic geometryrandom tessellationiteration/nesting of tessellationsSTIT tessellationspatial consistency

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60J75: Jump processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 47 , Issue 3 , September 2015 , pp. 640 - 651
Copyright
Copyright © Applied Probability Trust 2015 

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