Asymptotic statistics of then-sided planar Poisson–Voronoi cell: I. Exact results

DOI10.1088/1742-5468/2005/09/P09005zbMath1456.60040arXivcond-mat/0507567OpenAlexW3103183411MaRDI QIDQ4968881

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/0507567

zbMATH Keywords

networksrandom graphsrandom lattices (surfaces)

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (9)

Complex systems: features, similarity and connectivity ⋮ Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics ⋮ Shaping large Poisson Voronoi cells in two dimensions ⋮ 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 ⋮ Percolation on random Johnson-Mehl tessellations and related models ⋮ The maximal degree in a Poisson-Delaunay graph ⋮ 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
• Topological correlations in cellular structures and planar graph theory
• 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
• The perimeter of large planar Voronoi cells: a double-stranded random walk
• Random Distribution of Lines in a Plane

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