Many-faced cells and many-edged faces in 3D Poisson-Voronoi tessellations

H. J. Hilhorst, E. A. Lazar

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3 Scopus citations


Motivated by recent new Monte Carlo data we investigate a heuristic asymptotic theory that applies to n-faced 3D Poisson-Voronoi cells in the limit of large n. We show how this theory may be extended to n-edged cell faces. It predicts the leading order large-n behavior of the average volume and surface area of the n-faced cell, and of the average area and perimeter of the n-edged face. Such a face is shown to be surrounded by a toroidal region of volume n/λ (with λ the seed density) that is void of seeds. Two neighboring cells sharing an n-edged face are found to have their seeds at a typical distance that scales as n-1/6 and whose probability law we determine. We present a new data set of 4 ×.

Original languageEnglish
Article numberP10021
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number10
StatePublished - 1 Oct 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 IOP Publishing Ltd and SISSA Medialab srl.


  • Stochastic processes (theory)
  • extreme value statistics
  • networks
  • random graphs


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