M. Reitzner

activity

20052025

U

-statistics of Poisson point processes

131 citations · 244 across the 25 of their papers we have counts for

collaborators

34 papers

math.PR2025

Central limit theorems for random boundary polytopes

Matthias Reitzner, Mathias Sonnleitner

The number of faces of the convex hull of $n$ independent and identically distributed random points chosen on the boundary of a smooth convex body in $R^{d}$ is investigated…

math.PR2024

Poisson-Delaunay approximation

Matthias Reitzner, Anna Strotmann

For a Borel set $A$ and a stationary Poisson point process $η_{t}$ in $R^{d}$ of intensity $t > 0$ , the Poisson-Delaunay approximation $A_{η_{t}}$ of $A$ is the union of all Delau…

math.PR2022

Covariance matrices of length power functionals of random geometric graphs -- an asymptotic analysis

Matthias Reitzner, Tim Römer, Mandala von Westenholz

Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intens…

math.PR2022

Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon

Anna Gusakova, Matthias Reitzner, Christoph Thäle

Fix a container polygon $P$ in the plane and consider the convex hull $P_{n}$ of $n \geq 3$ independent and uniformly distributed in $P$ random points. In the focus of this paper is t…

math.PR2022

Spherical convex hull of random points on a wedge

Florian Besau, Anna Gusakova, Matthias Reitzner +3

Consider two half-spaces $H_{1}^{+}$ and $H_{2}^{+}$ in $R^{d + 1}$ whose bounding hyperplanes $H_{1}$ and $H_{2}$ are orthogonal and pass through the origin. The intersection $\mathbb{…

math.MG2020

Expected mean width of the randomized integer convex hull

Binh Hong Ngoc, Matthias Reitzner

Let $K \in R^{d}$ be a convex body, and assume that $L$ is a randomly rotated and shifted integer lattice. Let $K_{L}$ be the convex hull of the (random) points $K \cap L$ . The mean w…