2010/04/30 by Tomasz Schreiber, Schreiber, Tomasz, Natalia Soja +1
Computer Science · Engineering · Mathematics · #60D05 #60F05 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #math.PR #msc:60D05 #msc:60F05
paper · pdf · doi:10.48550/arxiv.1005.0023
12 pages
arxiv created 2010/04/30 · openalex publication_date 2010/04/30 · arxiv updated 2010/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.