J. Grote

activity

20152019

most citedThreshold phenomena for high-dimensional random polytopes

17 citations · 18 across the 3 of their papers we have counts for

collaborators

9 papers

math.MG2019

Asymptotic normality for random simplices and convex bodies in high dimensions

David Alonso-Gutiérrez, Florian Besau, Julian Grote +5

Central limit theorems for the log-volume of a class of random convex bodies in $R^{n}$ are obtained in the high-dimensional regime, that is, as $n \to \infty$ . In particular,…

math.MG2018

Surface area deviation between smooth convex bodies and polytopes

Julian Grote, Christoph Thaele, Elisabeth M. Werner

The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the…

math.PR2018

Universal Scaling Limits for Generalized Gamma Polytopes

Julian Grote

Fix a space dimension $d \geq 2$ , parameters $α > - 1$ and $β \geq 1$ , and let $γ_{d, α, β}$ be the probability measure of an isotropic random vector in $R^{d}$ with density propor…

math.MG2018★ 17 cited

Threshold phenomena for high-dimensional random polytopes

Gilles Bonnet, Giorgos Chasapis, Julian Grote +2

Let $X_{1}, \dots, X_{N}$ , $N > n$ , be independent random points in $R^{n}$ , distributed according to the so-called beta or beta-prime distribution, respectively. We establish thre…

math.PR2017

Limit theorems for random simplices in high dimensions

Julian Grote, Zakhar Kabluchko, Christoph Thäle

Let $r = r (n)$ be a sequence of integers such that $r \leq n$ and let $X_{1}, \dots, X_{r + 1}$ be independent random points distributed according to the Gaussian, the Beta or the spherica…

math.MG2017

Approximation of smooth convex bodies by random polytopes

Julian Grote, Elisabeth M. Werner

Let $K$ be a convex body in $R^{n}$ and $f : \partial K \to R_{+}$ a continuous, strictly positive function with $\int\limits_{\partial K} f(x) d μ_{\partial…

math.MG2017★ 1 cited

Monotonicity of facet numbers of random convex hulls

Gilles Bonnet, Julian Grote, Daniel Temesvari +3

Let $X_{1}, \dots, X_{n}$ be independent random points that are distributed according to a probability measure on $R^{d}$ and let $P_{n}$ be the random convex hull generated by $X_…

math.PR2016

Gaussian polytopes: a cumulant-based approach

Julian Grote, Christoph Thaele

The random convex hull of a Poisson point process in $R^{d}$ whose intensity measure is a multiple of the standard Gaussian measure on $R^{d}$ is investigated. The pu…

math.PR2015

Concentration and moderate deviations for Poisson polytopes and polyhedra

Julian Grote, Christoph Thaele

The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$ -dimensional Euclidean space is considered. By establishing sharp boun…