M. Reitzner

activity

20092012

most citedPoisson polytopes

33 citations · 50 across the 4 of their papers we have counts for

collaborators

4 papers

cs.CG2012

The monotonicity of f-vectors of random polytopes

Olivier Devillers, Marc Glisse, Xavier Goaoc +2

Let K be a compact convex body in Rd, let Kn be the convex hull of n points chosen uniformly and independently in K, and let fi(Kn) denote the number of i-dimensional faces of Kn.…

math.PR2012

Many empty triangles have a common edge

Imre Bárány, Jean-François Marckert, Matthias Reitzner

Given a finite point set $X$ in the plane, the degree of a pair ${x, y} \subset X$ is the number of empty triangles $t = co n v {x, y, z}$ , where empty means $t \cap X = {x, y, z}$ . Defin…

math.PR2010★ 33 cited

Poisson polytopes

Imre Bárány, Matthias Reitzner

We prove the central limit theorem for the volume and the $f$ -vector of the Poisson random polytope $Π_{η}$ in a fixed convex polytope $P \subset R^{d}$ . Here, $Π_{η}$ is the conv…

math.PR2009★ 17 cited

Poisson--Voronoi approximation

Matthias Heveling, Matthias Reitzner

Let $X$ be a Poisson point process and $K \subset R^{d}$ a measurable set. Construct the Voronoi cells of all points $x \in X$ with respect to $X$ , and denote by $v_{X} (K)$ the u…