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.

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APA

Lee, S. (2000). Rate of convergence of power-weighted Euclidean minimal spanning trees. Stochastic Processes and Their Applications, 86(1), 163–176. https://doi.org/10.1016/S0304-4149(99)00091-5

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