Asymptotics of power-weighted Euclidean functionals

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4 Citations (Scopus)

Abstract

Let {Xi:i≥1} be i.i.d. points in Rd, d≥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≤p<d, has been obtained. In this paper we show that the same type of result holds for 0<p<1.

Original languageEnglish
Pages (from-to)109-116
Number of pages8
JournalStochastic Processes and their Applications
Volume79
Issue number1
DOIs
Publication statusPublished - 1999 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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