### Abstract

Let P be the Poisson point process with intensity 1 in R ^{d} and let P_{n} be P∩[-n/2,n/2]^{d}. We obtain a strong invariance principle for the total length of the nearest-neighbor graph on P_{n}.

Original language | English |
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Pages (from-to) | 649-664 |

Number of pages | 16 |

Journal | Journal of Theoretical Probability |

Volume | 18 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Jul 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*,

*18*(3), 649-664. https://doi.org/10.1007/s10959-005-7253-8

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*Journal of Theoretical Probability*, vol. 18, no. 3, pp. 649-664. https://doi.org/10.1007/s10959-005-7253-8

**The invariance principle for the total length of the nearest-neighbor graph.** / Kim, Younghoon; Lee, Sung chul; Lin, Zhengyan; Wang, Wensheng.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The invariance principle for the total length of the nearest-neighbor graph

AU - Kim, Younghoon

AU - Lee, Sung chul

AU - Lin, Zhengyan

AU - Wang, Wensheng

PY - 2005/7/1

Y1 - 2005/7/1

N2 - Let P be the Poisson point process with intensity 1 in R d and let Pn be P∩[-n/2,n/2]d. We obtain a strong invariance principle for the total length of the nearest-neighbor graph on Pn.

AB - Let P be the Poisson point process with intensity 1 in R d and let Pn be P∩[-n/2,n/2]d. We obtain a strong invariance principle for the total length of the nearest-neighbor graph on Pn.

UR - http://www.scopus.com/inward/record.url?scp=25144480438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25144480438&partnerID=8YFLogxK

U2 - 10.1007/s10959-005-7253-8

DO - 10.1007/s10959-005-7253-8

M3 - Article

VL - 18

SP - 649

EP - 664

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 3

ER -