Length distributions of edges in planar stationary and isotropic STIT tessellations
type: Item
instance of: scholarly article
title: Length distributions of edges in planar stationary and isotropic STIT tessellations
zbMATH Open document ID: 1155.60005
DOI: 10.3103/S1068362307010025
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 2008-09-12T00:00:00Z
review text: The iteration operation for a planar tessellation is defined by subdividing its cells using a sequence of further iid tessellations. If the rescaled result of this (possibly iterated) operation coincides in distribution with the original tessellation \(\mathcal{Y}\), then \(\mathcal{Y}\) is said to be stable with respect to iteration (STIT) [see \textit{W. Nagel} and \textit{V. Weiss}, Adv. Appl. Probab. 37, 859--883 (2005; Zbl 1098.60012)]. The authors recall the construction of STIT tessellations in bounded windows, discuss properties of mean values and then proceed to study length distributions for segments of three different types that appear as edges of STIT tessellations. The authors derive explicit formulae for their length distributions in the stationary and isotropic case and discuss various properties of the obtained length distributions.
reviewed by: Ilya S. Molchanov
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 5343511
zbMATH Keywords: random tessellation
zbMATH Keywords: iteration of tessellations
zbMATH Keywords: stable tessellation
zbMATH Keywords: edge
author: J. Mecke
author: Werner Nagel
author: V. Weiss
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5343511