4 papers · 1 filter
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…
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…
The isotropic constant of random polytopes with vertices on convex surfaces
Joscha Prochno, Christoph Thäle, Nicola Turchi
For an isotropic convex body we consider the isotropic constant of the symmetric random polytope generated by independent random points w…
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}…