15 papers
Central limit theorems for the nearest neighbour embracing graph in Euclidean and hyperbolic space
Holger Sambale, Christoph Thäle, Tara Trauthwein
Consider a stationary Poisson process in the -dimensional Euclidean or hyperbolic space and construct a random graph with vertex set as follows. First, each point $x\inη…
The proportion of triangles in a class of anisotropic Poisson line tessellations
Nils Heerten, Julia Krecklenberg, Christoph Thäle
Stationary Poisson processes of lines in the plane are studied whose directional distributions are concentrated on equally spread directions. The random lines of such pro…
Second-order properties for planar Mondrian tessellations
Carina Betken, Tom Kaufmann, Kathrin Meier +1
In this paper planar STIT tesselations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tesselations in the machine le…
Spherical convex hull of random points on a wedge
Florian Besau, Anna Gusakova, Matthias Reitzner +3
Consider two half-spaces and in whose bounding hyperplanes and are orthogonal and pass through the origin. The intersection $\mathbb{…
Approaching the coupon collector's problem with group drawings via Stein's method
Carina Betken, Christoph Thäle
In this paper the coupon collector's problem with group drawings is studied. Assume there are different coupons. At each time precisely of the coupons are drawn,…
Random cones in high dimensions II: Weyl cones
Thomas Godland, Zakhar Kabluchko, Christoph Thäle
We consider two models of random cones together with their duals. Let be independent and identically distributed random vectors in whose distribution…