2013/12/02 by Werner Nagel, Nagel, Werner, Eike Biehler +1
Economics, Econometrics and Finance · Mathematics · #60D05 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Regional Economics and Spatial Analysis #Spatial and Panel Data Analysis #math.PR #msc:60D05
paper · pdf · doi:10.48550/arxiv.1312.0397
arxiv created 2013/12/02 · openalex publication_date 2013/12/02 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a class of cell division processes, generating tessellations of the Euclidean space ℝd, spatial consistency is investigated. This addresses the problem whether the distribution of these tessellations, 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. In Nagel and Weiß (2005) it was shown that the STIT tessellations are spatially consistent There were hints that the STIT tessellation process might be the only translation-invariant cell division process that has such a consistency property. 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.