4 citations · 9 across the 12 of their papers we have counts for
13 papers
Tessellation-valued processes that are generated by cell division
Servet Martínez, Werner Nagel
Processes of random tessellations of the Euclidean space , , are considered which are generated by subsequent division of their cells. Such processes are cha…
The largest order statistics for the inradius in an isotropic STIT tessellation
Nicolas Chenavier, Werner Nagel
A planar stationary and isotropic STIT tessellation at time is observed in the window , for . With each cell o…
Regenerative processes for Poisson zero polytopes
Servet Martínez, Werner Nagel
Let be a Markov process of tessellations of and the process of their zero cells (zero polytopes) which has the same distri…
Joseph Mecke's last fragmentary manuscripts - a compilation
Joseph Mecke, Werner Nagel, Viola Weiss
Summarizing results from Joseph Mecke's last fragmentary manuscripts, the generating function and the Laplace transform for nonnegative random variables are considered. The concept…
A Mecke-type formula and Markov properties for STIT tessellation processes
Werner Nagel, Linh Ngoc Nguyen, Christoph Thaele +1
An analogue of the classical Mecke formula for Poisson point processes is proved for the class of space-time STIT tessellation processes. From this key identity the Markov property…
STIT Tessellations -- Ergodic Limit Theorems and Bounds for the Speed of Convergence
Servet Martínez, Werner Nagel
We consider homogeneous STIT tessellations in the -dimensional Euclidean space . Based on results for the spatial -mixing coefficient an upper bound for…
STIT Process and Trees
Servet Martínez, Werner Nagel
We study several constructions of the STIT tessellation process in a window of $\RR^\ell$ and supply an exact formula for its transition probability.
On the capacity functional of excursion sets of Gaussian random fields on
Marie Kratz, Werner Nagel
When a random field is thresholded on a given level , the excursion set is given by its indicator . The purpose of this work…
The -Mixing Rate of STIT Tessellations
Servet Martínez, Werner Nagel
We consider homogeneous STIT tessellations in the -dimensional Euclidean space and show that the (spatial) -mixing rate converges to zero.
On the consistency of cell division processes
Werner Nagel, Eike Biehler
For a class of cell division processes, generating tessellations of the Euclidean space , spatial consistency is investigated. This addresses the problem whether the…
STIT Tessellations have trivial tail σ-algebra
Servet Martínez, Werner Nagel
We consider homogeneous STIT tessellations Y in the \ell-dimensional Euclidean space and show the triviality of the tail σ-algebra. This is a sharpening of the mixing result by Lac…
Spatial STIT Tessellations -- Distributional Results for I-Segments
Christoph Thaele, Viola Weiss, Werner Nagel
Three-dimensional random tessellations that are stable under iteration (STIT tessellations) are considered. They arise as a result of subsequent cell division, which implies that t…
Ergodic Description of STIT Tessellations
Servet Martínez, Werner Nagel
Let (Y_t: t > 0) be the STIT tessellation process. We show that for all polytopes W with nonempty interior and all a>1, the renormalized random sequence (a^n Y_{a^n}: n integer) in…