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Asymptotics of power-weighted Euclidean functionals

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  • Lee, Sungchul

Abstract

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. points in , d[greater-or-equal, slanted]2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with weight function w(e)=ep. If the common distribution satisfies certain regularity conditions, then the strong law of large numbers for the above three Euclidean functionals, 1[less-than-or-equals, slant]p

Suggested Citation

  • Lee, Sungchul, 1999. "Asymptotics of power-weighted Euclidean functionals," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 109-116, January.
  • Handle: RePEc:eee:spapps:v:79:y:1999:i:1:p:109-116
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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. Lee, Sungchul, 2000. "Rate of convergence of power-weighted Euclidean minimal spanning trees," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 163-176, March.
    2. Yooyoung Koo & Sungchul Lee, 2007. "Rates of Convergence of Means of Euclidean Functionals," Journal of Theoretical Probability, Springer, vol. 20(4), pages 821-841, December.
    3. Yukich, J. E., 2000. "Asymptotics for weighted minimal spanning trees on random points," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 123-138, January.

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