Gilles Bonnet

activity

20162026

most citedThreshold phenomena for high-dimensional random polytopes

17 citations · 38 across the 9 of their papers we have counts for

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5 papers · 1 filter

math.MG2020★ 4 cited

Sharp inequalities for the mean distance of random points in convex bodies

Gilles Bonnet, Anna Gusakova, Christoph Thäle +1

For a convex body $K \subset R^{d}$ the mean distance $Δ (K) = E ∣ X_{1} - X_{2} ∣$ is the expected Euclidean distance of two independent and uniformly distributed random points…

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.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.MG2017★ 4 cited

Small cells in a Poisson hyperplane tessellation

Gilles Bonnet

Until now, little was known about properties of small cells in a Poisson hyperplane tessellation. The few existing results were either heuristic or applying only to the two dimensi…

math.MG2016

Polytopal approximation of elongated convex bodies

Gilles Bonnet

This paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex body $K$ by a circumscribed polytope $P$ with a given number of facets. The…