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On variances of partial volumes of the typical cell of a Poisson-Voronoi tessellation and large-dimensional volume degeneracy

  • Yi-Ching Yao (a1)

Abstract

For a typical cell of a homogeneous Poisson-Voronoi tessellation in ℝ d , it is shown that the variance of the volume of the intersection of the typical cell with any measurable subset of ℝ d is bounded by the variance of the volume of the typical cell. It is also shown that the variance of the volume of the intersection of the typical cell with a translation of itself is bounded by four times the variance of the volume of the typical cell. These bounds are applied to show large-dimensional volume degeneracy as d tends to ∞. An extension to the kth nearest-point Poisson-Voronoi tessellation for k ≥ 2 is also considered.

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Copyright

Corresponding author

Postal address: Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan, R.O.C. Email address: yao@stat.sinica.edu.tw

References

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On variances of partial volumes of the typical cell of a Poisson-Voronoi tessellation and large-dimensional volume degeneracy

  • Yi-Ching Yao (a1)

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