8 papers
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{…
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…
Asymptotic normality for random polytopes in non-Euclidean geometries
Florian Besau, Christoph Thäle
Asymptotic normality for the natural volume measure of random polytopes generated by random points distributed uniformly in a convex body in spherical or hyperbolic spaces is prove…
Asymptotic normality for random simplices and convex bodies in high dimensions
David Alonso-Gutiérrez, Florian Besau, Julian Grote +5
Central limit theorems for the log-volume of a class of random convex bodies in are obtained in the high-dimensional regime, that is, as . In particular,…
Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes
Florian Besau, Steven Hoehner, Gil Kur
We establish estimates for the asymptotic best approximation of the Euclidean unit ball by polytopes under a notion of distance induced by the intrinsic volumes. We also introduce…
Spherical centroid bodies
Florian Besau, Thomas Hack, Peter Pivovarov +1
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in…