Elongated Poisson-Voronoi cells in an empty half-plane - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2022

Elongated Poisson-Voronoi cells in an empty half-plane

Résumé

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 of these cells is ruled by a Markovian branching mechanism which is asymptotically described by two sequences of iid variables which are respectively Beta and exponentially distributed. This leads to a precise description of the scaling limit of a so-called typical cell. The limit object is a random apeirogon that we name menhir in reference to the Gallic huge stones. We also deduce from the aforementioned branching mechanism that the number of vertices of a cell of height $\lambda$ is asymptotically equal to $\frac45\log\lambda$.
Fichier principal
Vignette du fichier
PVDeep_2.pdf (2.11 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03613908 , version 1 (18-03-2022)

Identifiants

Citer

Pierre Calka, Yann Demichel, Nathanaël Enriquez. Elongated Poisson-Voronoi cells in an empty half-plane. Advances in Mathematics, 2022, 410 (Part A), ⟨10.48550/arXiv.2203.10806⟩. ⟨hal-03613908⟩
108 Consultations
45 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More