Finding the area and perimeter distributions for flat Poisson processes of a straight line and Voronoi diagrams

DOI10.1134/s1064562424701801zbMATH Open1540.60024MaRDI QIDQ6545172

R. P. Yavich, Alexei Kanel-Belov, Sergey Malev, M. M. Golafshan

Publication date: 29 May 2024

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

kinetic equationVoronoi diagramrandom setsstatistical geometryMarkov equationPoisson line processgeometric probabilitiesdistributions of random variables

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Cites Work

• Unnamed Item
• Angles of random simplices and face numbers of random polytopes
• 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
• Poisson flats in Euclidean spaces Part I: A finite number of random uniform flats
• The Random Division of Space

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