Rates of convergence of means of euclidean functionals

Yooyoung Koo, Sung chul Lee

Research output: Contribution to journalArticle

4 Citations (Scopus)

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,â,X n } from [0,1] d , L({X 1,â,X n })/n (d-p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X 1,â,X n })/n (d-p)/d .

Original languageEnglish
Pages (from-to)821-841
Number of pages21
JournalJournal of Theoretical Probability
Volume20
Issue number4
DOIs
Publication statusPublished - 2007 Dec 1

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Minimal Spanning Tree
Travelling salesman
Sample point
Euclidean
Rate of Convergence
Converge
Rate of convergence
Spanning tree
Traveling salesman

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Cite this

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Rates of convergence of means of euclidean functionals. / Koo, Yooyoung; Lee, Sung chul.

In: Journal of Theoretical Probability, Vol. 20, No. 4, 01.12.2007, p. 821-841.

Research output: Contribution to journalArticle

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