The perimeter of large planar Voronoi cells: a double-stranded random walk

DOI10.1088/1742-5468/2005/02/L02003zbMath1459.60023arXivcond-mat/0412569MaRDI QIDQ4968830

Hendrik Jan Hilhorst

Publication date: 9 July 2019

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0412569

zbMATH Keywords

networksrandom graphsfoamsexact resultsstructural correlations (theory)

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random graphs (graph-theoretic aspects) (05C80)

Related Items (8)

Complex systems: features, similarity and connectivity ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics ⋮ Heuristic theory for many-facedd-dimensional Poisson–Voronoi cells ⋮ Large-nconditional facednessm_nof 3D Poisson–Voronoi cells ⋮ Exact asymptotic statistics of the n-edged face in a 3D Poisson-Voronoi tessellation ⋮ Exponential moments for planar tessellations ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: I. Exact results ⋮ Sylvester’s question and the random acceleration process

Cites Work

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• Radial generation of n-dimensional poisson processes
• Statistical Field Theory
• An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell
• Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process
• The proportion of triangles in a Poisson-Voronoi tessellation of the plane
• Large Poisson-Voronoi cells and Crofton cells
• The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
• A comment on Rivier's maximum entropy method of statistical crystallography

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