Rates of convergence of means of euclidean functionals

Yooyoung Koo, Sungchul Lee

Research output: Contribution to journalArticlepeer-review

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

Bibliographical note

Funding Information:
Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.

All Science Journal Classification (ASJC) codes

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

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