### 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 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Koo, Y., & Lee, S. (2007). Rates of convergence of means of euclidean functionals.

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