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On the size distribution of Poisson Voronoi cells

Author

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  • Ferenc, Járai-Szabó
  • Néda, Zoltán

Abstract

Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three-dimensional (3D) spaces there is no exact result known for the size distribution of Voronoi cells. Motivated by the simple form of the distribution function in the 1D case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well. Denoting the dimensionality of the space by d (d=1,2,3) the f(y)=Const*y(3d-1)/2exp(-(3d+1)y/2) compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the viability of the proposed distribution function is studied and critically discussed.

Suggested Citation

  • Ferenc, Járai-Szabó & Néda, Zoltán, 2007. "On the size distribution of Poisson Voronoi cells," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 518-526.
    • Handle: RePEc:eee:phsmap:v:385:y:2007:i:2:p:518-526
    DOI: 10.1016/j.physa.2007.07.063
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    Citations

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    Cited by:

    1. Hiroyuki Usui, 2018. "Statistical distribution of building lot frontage: application for Tokyo downtown districts," Journal of Geographical Systems, Springer, vol. 20(3), pages 295-316, July.
    2. Uhlmann, Markus, 2020. "Voronoï tessellation analysis of sets of randomly placed finite-size spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    3. Hafver, Andreas & Jettestuen, Espen & Baetens, Jan M. & Malthe-Sørenssen, Anders, 2014. "Network formation by contact arrested propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 240-255.
    4. Zhu, H.X. & Zhang, P. & Balint, D. & Thorpe, S.M. & Elliott, J.A. & Windle, A.H. & Lin, J., 2014. "The effects of regularity on the geometrical properties of Voronoi tessellations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 42-58.
    5. Stegehuis, Clara & Weedage, Lotte, 2022. "Degree distributions in AB random geometric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    6. Yangyang Chen & Feng Yan & Xavier Lagrange, 2017. "Performance analysis of cellular networks with mobile relays under different modes," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 66(2), pages 217-231, October.
    7. Hiroyuki Usui, 2018. "Estimation of geometric route distance from its topological distance: application to narrow road networks in Tokyo," Journal of Geographical Systems, Springer, vol. 20(4), pages 387-412, October.

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