We study random polytopes of the form [X 1,…, X n] defined as convex hulls of independent
and identically distributed random points X 1,…, X n in R d with one of the following …

Motivated by problems of hyperbolic stochastic geometry we introduce and study the class of
beta-star polytopes. A beta-star polytope is defined as the convex hull of an inhomogeneous …

Pick d+ 1 points uniformly at random on the unit sphere in R d. What is the expected value of
the angle sum of the simplex spanned by these points? Choose n points uniformly at …

Poisson processes in the space of (d-1)(d-1)-dimensional totally geodesic subspaces
(hyperplanes) in ad-dimensional hyperbolic space of constant curvature-1-1 are studied …

This book provides the foundations for geometric applications of convex cones and presents
selected examples from a wide range of topics, including polytope theory, stochastic …

Let $ M $ be an arbitrary subset in $\mathbb R^ n $ with a conic (or positive) hull $ C $.
Consider its Gaussian image $ AM $, where $ A $ is a $ k\times n $-matrix whose entries are …

We study measures and point configurations optimizing energies based on multivariate
potentials. The emphasis is put on potentials defined by geometric characteristics of sets of …

We prove an explicit combinatorial formula for the expected number of faces of the zero
polytope of the homogeneous and isotropic Poisson hyperplane tessellation in R d. The …

The beta polytope is the convex hull of n iid random points distributed in the unit ball of
according to a density proportional to if (in particular, corresponds to the uniform distribution …

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 …