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math.PR2024
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…
math.PR2022
Elongated Poisson-Voronoi cells in an empty half-plane
Pierre Calka, Yann Demichel, Nathanaël Enriquez
The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges…