Rate of convergence of power-weighted Euclidean minimal spanning trees

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Abstract

Let {Xi:i1} be i.i.d. uniform points on [-1/2,1/2]d, d2, and for 0<p<∞. Let L({X1,Xn},p) be the total weight of the minimal spanning tree on {X1,Xn} with weight function w(e)=|e|p. Then, there exist strictly positive but finite constants β(d,p), C3=C3(d,p), and C4=C4(d,p) such that for large n, C3n-1/d≤EL({X1,Xn},p)/n (d-p)/d-β(d,p)≤C4n-1/d.

Original languageEnglish
Pages (from-to)163-176
Number of pages14
JournalStochastic Processes and their Applications
Volume86
Issue number1
DOIs
Publication statusPublished - 2000 Mar

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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