2005/09/15 by H. J. Hilhorst, Hendrik-Jan Hilhorst, Hilhorst, Hendrik-Jan
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Computational Geometry and Mesh Generation #FOS: Physical sciences #Point processes and geometric inequalities #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0509409
arxiv created 2005/09/15 · openalex publication_date 2005/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Aboav's law is a quantitative expression of the empirical fact that in planar cellular structures many-sided cells tend to have few-sided neighbors. This law is nonetheless violated in the most widely used model system, \it viz. the Poisson-Voronoi tessellation. We obtain the correct law for this model: Given an n-sided cell, any of its neighbors has on average m_n sides where m_n=4+3(π/n)^-1/2+... in the limit of large n. This expression is quite accurate also for nonasymptotic n and we discuss its implications for the analysis of experimental data.