Gilles Bonnet

activity

20182020

collaborators

5 papers

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

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

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…