5 papers
Random inscribed polytopes in projective geometries
Florian Besau, Daniel Rosen, Christoph Thäle
We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volu…
Limit theorems for random points in a simplex
Anastas Baci, Zakhar Kabluchko, Joscha Prochno +2
In this work the -norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry-Esseen bounds in the regime $1\leq q < \inf…
Does a central limit theorem hold for the -skeleton of Poisson hyperplanes in hyperbolic space?
Felix Herold, Daniel Hug, Christoph Thähle
Poisson processes in the space of -dimensional totally geodesic subspaces (hyperplanes) in a -dimensional hyperbolic space of constant curvature are studied. The …
Surface area deviation between smooth convex bodies and polytopes
Julian Grote, Christoph Thaele, Elisabeth M. Werner
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the…
Expected intrinsic volumes and facet numbers of random beta-polytopes
Zakhar Kabluchko, Daniel Temesvari, Christoph Thaele
Let be i.i.d.\ random points in the -dimensional Euclidean space sampled according to one of the following probability densities: $$ f_{d,β} (x) = \text{const}…