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Strong laws for Euclidean graphs with general edge weights

Author

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  • Jiménez, Raúl
  • Yukich, J. E.

Abstract

Consider a random Euclidean graph G with a vertex set consisting of i.i.d. random variables with a common density f. Let the edge lengths e, e[set membership, variant]G, be weighted by a function [phi]. We provide sufficient conditions on G and [phi] guaranteeing that the total edge length functional [summation operator]e[set membership, variant]G [phi](e) satisfies a strong law of large numbers. The limiting constant is shown to depend explicitly on f and [phi].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:3:p:251-259
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Liu, Yehong & Yin, Guosheng, 2020. "The Delaunay triangulation learner and its ensembles," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

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