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

collaborators

13 papers

math.PR2026

Wasserstein stability of the zero cell of a Poisson hyperplane tessellation under directional perturbations

Gilles Bonnet, Eliza O'Reilly, Bharath Roy Choudhury

A stationary Poisson hyperplane process in $R^{d}$ is characterized by an intensity parameter and an even probability measure on the unit sphere called the directional distr…

math.PR2022★ 2 cited

Limit theory of sparse random geometric graphs in high dimensions

Gilles Bonnet, Christian Hirsch, Daniel Rosen +1

We study topological and geometric functionals of $l_{\infty}$ -random geometric graphs on the high-dimensional torus in a sparse regime, where the expected number of neighbors decays…

math.PR2021

Asymptotic Bounds on the Combinatorial Diameter of Random Polytopes

Gilles Bonnet, Daniel Dadush, Uri Grupel +2

The combinatorial diameter $diam (P)$ of a polytope $P$ is the maximum shortest path distance between any pair of vertices. In this paper, we provide upper and lower…

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.PR2020

Weak convergence of the intersection point process of Poisson hyperplanes

Anastas Baci, Gilles Bonnet, Christoph Thäle

This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $R^{d}$ of intensity $t > 0$ , where only hyperplanes that inte…

math.PR2019★ 10 cited

Phase transition for the volume of high-dimensional random polytopes

Gilles Bonnet, Zakhar Kabluchko, Nicola Turchi

The beta polytope $P_{n, d}^{β}$ is the convex hull of $n$ i.i.d. random points distributed in the unit ball of $R^{d}$ according to a density proportional to $(1-\lVert{x}\rVe…

math.PR2019

Facets of spherical random polytopes

Gilles Bonnet, Eliza O'Reilly

Facets of the convex hull of $n$ independent random vectors chosen uniformly at random from the unit sphere in $R^{d}$ are studied. A particular focus is given on the height…

math.PR2018

The maximal degree in a Poisson-Delaunay graph

Gilles Bonnet, Nicolas Chenavier

We investigate the maximal degree in a Poisson-Delaunay graph in $R^{d}$ , $d \geq 2$ , over all nodes in the window $W_{ρ} := ρ^{1/ d} [0, 1]^{d}$ as $ρ$ goes to infinity. Th…

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…

math.PR2016

Cells with many facets in a Poisson hyperplane tessellation

Gilles Bonnet, Pierre Calka, Matthias Reitzner

Let $Z$ be the typical cell of a stationary Poisson hyperplane tessellation in $R^{d}$ . The distribution of the number of facets $f (Z)$ of the typical cell is investigated.…