A global construction of homogeneous random planar tessellations that are stable under iteration
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Publication:5451160
DOI10.1080/17442500701605403zbMath1139.60011OpenAlexW1974047745MaRDI QIDQ5451160
Viola Weiß, Werner Nagel, Joseph Mecke
Publication date: 18 March 2008
Published in: Stochastics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/17442500701605403
Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)
Related Items (18)
Spatial Stit Tessellations: Distributional Results for I-Segments ⋮ Stit Tessellations have Trivial Tail σ-Algebra ⋮ A stochastic model for multi-hierarchical networks ⋮ Limit theorems for iteration stable tessellations ⋮ Second-order properties for planar Mondrian tessellations ⋮ Geometry of iteration stable tessellations: connection with Poisson hyperplanes ⋮ Proofs of the conjectures by Mecke for mixed line-generated tessellations ⋮ Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration ⋮ The iteration of random tessellations and a construction of a homogeneous process of cell divisions ⋮ Mixing properties for STIT tessellations ⋮ Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations ⋮ A Mecke-type formula and Markov properties for STIT tessellation processes ⋮ The largest order statistics for the inradius in an isotropic STIT tessellation ⋮ Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane ⋮ Regenerative processes for Poisson zero polytopes ⋮ Some distributions for I-segments of planar random homogeneous STIT tessellations ⋮ Line Segments in the Isotropic Planar Stit Tessellation ⋮ Branching random tessellations with interaction: a thermodynamic view
Cites Work
- Convergence and existence of random set distributions
- An introduction to the theory of point processes
- Limits of sequences of stationary planar tessellations
- Stationary iterated tessellations
- Theory of Random Sets
- Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration
- Random Fragmentation and Coagulation Processes
- [https://portal.mardi4nfdi.de/wiki/Publication:5549427 Station�re zuf�llige Ma�e auf lokalkompakten Abelschen Gruppen]
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