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M. Reitzner

Publications and source records attributed to M. Reitzner.

2 recordsLinked to original sources
arXiv2019

Multivariate Central Limit Theorems for Random Simplicial Complexes

Consider a Poisson point process within a convex set in a Euclidean space. The Vietoris-Rips complex is the clique complex over the graph connecting all pairs of points with distance at most $\delta$. Summing powers of the volume of all $k$-dimensional faces defines the volume-power functionals of these random simplicial complexes. The asymptotic behavior of the volume-power functionals of the Vietoris-Rips complex is investigated as the intensity of the underlying Poisson point process tends to infinity and the distance parameter goes to zero. Univariate and multivariate central limit theorems are proven. Analogous results for the \v{C}ech complex are given.

math.PR↗
arXiv2019

The convex hull of random points on the boundary of a simple polytope

The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are derived. This is one of the first investigations leading to rigorous results for random polytopes which are neither simple nor simplicial. The results contrast existing results when points are chosen in the interior of a convex set.

math.PR↗