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Random hyperbolic polyhedra in horoballs
Florian Besau, Anna Gusakova, Christoph Thäle
We study the geodesic convex hull of a stationary Poisson point process restricted to a horoball in -dimensional hyperbolic space. The resulting random set is an unbounded hyper…
Lengths and incidences in Poisson hypersphere and spherical splitting tessellations
Daniel Hug, Christoph Thäle
We investigate distributional properties of two random tessellation models on the -dimen\-sional unit sphere. First, we analyze the Poisson hypersphere tessellation generated by…
Realising atomless laws as distance distributions on metric measure spaces
Christoph Thäle, Philipp Tuchel
We study which probability measures on can occur as the distribution of the distance between two independent points sampled from a complete separable metric space equi…
Mod-phi convergence for random variables with cyclotomic generating functions
Christoph Thäle, Philipp Tuchel
We consider a sequence of discrete random variables whose generating functions are polynomials only having roots on the unit circle in the complex plane. For such sequences we prov…