Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 47, Number 3 (2015), 640-651.
Consistency of constructions for cell division processes
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.
Adv. in Appl. Probab., Volume 47, Number 3 (2015), 640-651.
First available in Project Euclid: 8 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60J75: Jump processes
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