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Asymptotics for Voronoi tessellations on random samples

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  • McGivney, K.
  • Yukich, J. E.

Abstract

Let V(X1,...,Xn) denote the total edge length of the Voronoi tessellation on random variables X1,...,Xn. If X1,X2,... are independent and have a common continuous density f(x) on the unit square which is bounded away from 0 and [infinity] then it is shown thatwhere c.c. denotes complete convergence.

Suggested Citation

  • McGivney, K. & Yukich, J. E., 1999. "Asymptotics for Voronoi tessellations on random samples," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 273-288, October.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:2:p:273-288
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    References listed on IDEAS

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    1. Redmond, C. & Yukich, J. E., 1996. "Asymptotics for Euclidean functionals with power-weighted edges," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 289-304, February.
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    Cited by:

    1. R. Jiménez & J. E. Yukich, 2002. "Asymptotics for Statistical Distances Based on Voronoi Tessellations," Journal of Theoretical Probability, Springer, vol. 15(2), pages 503-541, April.
    2. Jiménez, Raúl & Yukich, J. E., 2002. "Strong laws for Euclidean graphs with general edge weights," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 251-259, February.

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