### 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 |
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Pages (from-to) | 821-841 |

Number of pages | 21 |

Journal | Journal of Theoretical Probability |

Volume | 20 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2007 Dec 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Theoretical Probability*,

*20*(4), 821-841. https://doi.org/10.1007/s10959-007-0089-7

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*Journal of Theoretical Probability*, vol. 20, no. 4, pp. 821-841. https://doi.org/10.1007/s10959-007-0089-7

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Rates of convergence of means of euclidean functionals

AU - Koo, Yooyoung

AU - Lee, Sung chul

PY - 2007/12/1

Y1 - 2007/12/1

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 .

UR - http://www.scopus.com/inward/record.url?scp=35548997849&partnerID=8YFLogxK

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U2 - 10.1007/s10959-007-0089-7

DO - 10.1007/s10959-007-0089-7

M3 - Article

VL - 20

SP - 821

EP - 841

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 4

ER -