131 citations · 244 across the 25 of their papers we have counts for
5 papers · 1 filter
Monotonicity of the Sample Range of 3-D Data: Moments of Volumes of Random Tetrahedra
Stefan Kunis, Benjamin Reichenwallner, Matthias Reitzner
The sample range of uniform random points chosen in a given convex set is the convex hull . It is shown that in dimension three the…
On the cells in a stationary Poisson hyperplane mosaic
Matthias Reitzner, Rolf Schneider
Let be the mosaic generated by a stationary Poisson hyperplane process in . Under some mild conditions on the spherical directional distribution of $\ha…
Cells with many facets in a Poisson hyperplane tessellation
Gilles Bonnet, Pierre Calka, Matthias Reitzner
Let be the typical cell of a stationary Poisson hyperplane tessellation in . The distribution of the number of facets of the typical cell is investigated.…
Expected Sizes of Poisson-Delaunay Mosaics and Their Discrete Morse Functions
Herbert Edelsbrunner, Anton Nikitenko, Matthias Reitzner
Mapping every simplex in the Delaunay mosaic of a discrete point set to the radius of the smallest empty circumsphere gives a generalized discrete Morse function. Choosing the poin…
On the monotonicity of the moments of volumes of random simplices
Benjamin Reichenwallner, Matthias Reitzner
In a -dimensional convex body random points are chosen. Their convex hull is a random simplex. The expected volume of a random simplex is monotone under se…