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Asymptotics for Euclidean functionals with power-weighted edges

Author

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  • Redmond, C.
  • Yukich, J. E.

Abstract

We provide general and relatively simple conditions under which Euclidean functionals Lp on [0, 1]d with pth power-weighted edges satisfy the limit where Xi, i >= 1, are i.i.d. random variables with values in [0, 1]d, 0

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:2:p:289-304
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    References listed on IDEAS

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    1. Michel X. Goemans & Dimitris J. Bertsimas, 1991. "Probabilistic Analysis of the Held and Karp Lower Bound for the Euclidean Traveling Salesman Problem," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 72-89, February.
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    Cited by:

    1. Leonenko, Nikolaj & Seleznjev, Oleg, 2010. "Statistical inference for the [epsilon]-entropy and the quadratic Rényi entropy," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1981-1994, October.
    2. 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.
    3. 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.
    4. 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.
    5. Lee, Sungchul, 1999. "Asymptotics of power-weighted Euclidean functionals," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 109-116, January.
    6. 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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