Rates of Convergence of Means of Euclidean Functionals

Yooyoung Koo and Sungchul Lee ()
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Yooyoung Koo: Sungkyunkwan University
Sungchul Lee: Yonsei University

Journal of Theoretical Probability, 2007, vol. 20, issue 4, 821-841

Abstract: 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 (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X 1,…,X n } from [0,1] d , L({X 1,…,X n })/n (d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X 1,…,X n })/n (d−p)/d .

Keywords: Rate of convergence; Minimal matching; Minimal spanning tree; Traveling salesman problem (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0089-7

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