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Rates of convergence of means of Euclidean functionals

By Yooyoung Koo and Sungchul Lee

Abstract

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (1994, 1996) have shown that for n i.i.d. sample points {X1,...,Xn} from [0,1] d, L({X1,...,Xn})/n (d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X1,...,Xn})/n (d−p)/d

Year: 2012
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