Rates of convergence of means of euclidean functionals

Yooyoung Koo; Sungchul Lee

doi:10.1007/s10959-007-0089-7

Rates of convergence of means of euclidean functionals

Yooyoung Koo, Sungchul Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	821-841
Number of pages	21
Journal	Journal of Theoretical Probability
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s10959-007-0089-7
Publication status	Published - 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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10.1007/s10959-007-0089-7

Cite this

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

author = "Yooyoung Koo and Sungchul Lee",

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AU - Lee, Sungchul

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N2 - 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 .

AB - 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 .

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Rates of convergence of means of euclidean functionals

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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