4 papers · 1 filter
Sharp asymptotics for the maximal distance from the boundary to the nucleus of a typical Poisson-Voronoi cell
Pierre Calka, Cecilia d'Errico, Nathanaël Enriquez
We consider the typical Poisson-Voronoi cell in the Euclidean space R d and in particular the maximal distance D from a vertex of that cell to its nucleus. We provide a sharp asymp…
Fractal random sets associated with multitype Galton-Watson trees
Pierre Calka, Yann Demichel
In this paper, we consider a regular tessellation of the Euclidean plane and the sequence of its geometric scalings by negative powers of a fixed integer. We generate iteratively r…
Limit theory for the first layers of the random convex hull peeling in a simple polytope
Pierre Calka, Gauthier Quilan
The convex hull peeling of a point set consists in taking the convex hull, then removing the extreme points and iterating that procedure until no point remains. The boundary of eac…
The support function of the high-dimensional Poisson polytope
Pierre Calka, Benjamin Dadoun
Let be the convex hull of the intersection of the homogeneous Poisson point process of intensity in , , with the Euclidean unit ball $\mathbb{B…