Poisson processes in the space of k-dimensional totally geodesic subspaces (k-flats) in a d-
dimensional standard space of constant curvature κ∈{− 1, 0, 1} are studied, whose …

The union of the particles of a stationary Poisson process of compact (convex) sets in
Euclidean space is called Boolean model and is a classical topic of stochastic geometry. In …

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 …

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 …

Poisson processes of so-called $\lambda $-geodesic hyperplanes in $ d $-dimensional
hyperbolic space are studied for $0\leq\lambda\leq 1$. The case $\lambda= 0$ corresponds …

Consider a stationary Poisson process $\eta $ in a $ d $-dimensional hyperbolic space of
constant curvature $-\varkappa $ and let the points of $\eta $ together with a fixed origin $ o …

Consider the $ d $-dimensional hyperbolic space $\mathbb {M} _K^ d $ of constant
curvature $ K< 0$ and fix a point $ o $ playing the role of an origin. Let $\mathbf {L} $ be a …

We consider a Poisson point process on the space of lines in\mathbb R^ d, where a
multiplicative factor u> 0 of the intensity measure determines the density of lines. Each line …

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson
point process on the hyperbolic plane. We show that the critical probability for the existence …

Consider a stationary Poisson process of horospheres in ad-dimensional hyperbolic space.
In the focus of this note is the total surface area these random horospheres induce in a …