Advances in Applied Probability

Consistency of constructions for cell division processes

Werner Nagel and Eike Biehler

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Abstract

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 WV 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.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 3 (2015), 640-651.

Dates
First available in Project Euclid: 8 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1444308875

Digital Object Identifier
doi:10.1239/aap/1444308875

Mathematical Reviews number (MathSciNet)
MR3406601

Zentralblatt MATH identifier
1366.60030

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60J75: Jump processes

Keywords
Stochastic geometry random tessellation iteration/nesting of tessellations STIT tessellation spatial consistency

Citation

Nagel, Werner; Biehler, Eike. Consistency of constructions for cell division processes. Adv. in Appl. Probab. 47 (2015), no. 3, 640--651. doi:10.1239/aap/1444308875. https://projecteuclid.org/euclid.aap/1444308875


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