Length distributions of edges in planar stationary and isotropic STIT tessellations
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.
scientific article; zbMATH DE number 5343511
scientific article