Mareen Beermann

activity

20122017

most citedMonotonicity of functionals of random polytopes

2 citations · 2 across the 2 of their papers we have counts for

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math.PR2017★ 2 cited

Monotonicity of functionals of random polytopes

Mareen Beermann, Matthias Reitzner

The convex hull $P_{n}$ of a Gaussian sample $X_{1}, ..., X_{n}$ in $R^{d}$ is a Gaussian polytope. We prove that the expected number of facets $E f_{d - 1} (P_{n})$ is monotonically inc…

math.PR2014

Beyond the Efron-Buchta identities: distributional results for Poisson polytopes

Mareen Beermann, Matthias Reitzner

Let $Π$ be a random polytope defined as the convex hull of the points of a Poisson point process. Identities involving the moment generating function of the measure of $Π$ , the num…

math.PR2012

Asymptotic shape of small cells

Mareen Beermann, Claudia Redenbach, Christoph Thaele

A stationary Poisson line tessellation is considered whose directional distribution is concentrated on two different atoms with some positive weights. The shape of the typical cell…