3 papers
math.PR2019
Convex hulls of perturbed random point sets
Pierre Calka, J. E. Yukich
We consider the convex hull of the perturbed point process comprised of i.i.d. points, each distributed as the sum of a uniform point on the unit sphere and a uniform…
math.PR2016
The Poisson-Voronoi cell around an isolated nucleus
Pierre Calka, Yann Demichel, Nathanaël Enriquez
Consider a planar random point process made of the union of a point (the origin) and of a Poisson point process with a uniform intensity outside a deterministic set surrounding the…
math.PR2012
Variance asymptotics for random polytopes in smooth convex bodies
Pierre Calka, J. E. Yukich
Let be a smooth convex set and let $¶_\la$ be a Poisson point process on of intensity $\la$. The convex hull of $¶_\la \cap K$ is a random convex polytope $…