Random Cluster Tessellations

TL;DR

This paper introduces a generic point process-based approach to generate discrete random tilings, including Voronoi and Delone structures, by replacing convex polytopes with their vertices, with three illustrative constructions.

Contribution

It presents a novel, elementary method to produce random tilings using point process theory, expanding the toolkit for stochastic geometric structures.

Findings

Provides three explicit constructions of random tilings

Demonstrates how to generate Voronoi and Delone tilings randomly

Introduces a unified approach using point process theory

Abstract

This article describes, in elementary terms, a generic approach to produce discrete random tilings and similar random structures by using point process theory. The standard Voronoi and Delone tilings can be constructed in this way. For this purpose, convex polytopes are replaced by their vertex sets. Three explicit constructions are given to illustrate the concept.