2007/12/11 by Kai Matzutt, Matzutt, Kai
Materials Science · Mathematics · #52C23 #60D05 #82D25 #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #Quasicrystal Structures and Properties #math.MG #math.PR #msc:52C23 #msc:60D05 #msc:82D25
paper · pdf · doi:10.48550/arxiv.0712.1684
14 pages, 13 figures
arxiv created 2007/12/11 · openalex publication_date 2007/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.