## Abstract

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 language | English |
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Article number | P10021 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2014 |

Issue number | 10 |

DOIs | |

State | Published - 1 Oct 2014 |

Externally published | Yes |

### Bibliographical note

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

## Keywords

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