Poisson-Delaunay Mosaics of Order $k$

Abstract

The order-$k$ Voronoi tessellation of a locally finite set $X\subseteq {\mathbb{R}}^n$ decomposes ${\mathbb{R}}^n$ into convex domains whose points have the same $k$ nearest neighbors in $X$. Assuming $X$ is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the $k$ nearest points in $X$ are within a given distance threshold.

11 pages. Discrete & Computational Geometry (2018)

References in corpus (1)

• Expected Sizes of Poisson-Delaunay Mosaics and Their Discrete Morse Functions

Cited by in corpus (1)

• On the Size of Chromatic Delaunay Mosaics