13 citations · 62 across the 26 of their papers we have counts for
11 papers · 1 filter
Random zonotopes and valuations
Rolf Schneider
We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine…
Another look at threshold phenomena for random cones
Daniel Hug, Rolf Schneider
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passe…
Threshold phenomena for random cones
Daniel Hug, Rolf Schneider
We consider an even probability distribution on the -dimensional Euclidean space with the property that it assigns measure zero to any hyperplane through the origin. Given i…
Poisson hyperplane processes and approximation of convex bodies
Daniel Hug, Rolf Schneider
A natural model for the approximation of a convex body in by random polytopes is obtained as follows. Take a stationary Poisson hyperplane process in the space,…
Interaction of Poisson hyperplane processes and convex bodies
Rolf Schneider
Given a stationary and isotropic Poisson hyperplane process and a convex body in , we consider the random polytope defined by the intersection of all closed half…
The polytopes in a Poisson hyperplane tessellation
Rolf Schneider
For a stationary Poisson hyperplane tessellation in , whose directional distribution satisfies some mild conditions (which hold in the isotropic case, for exampl…