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

Younghoon Kim; Sungchul Lee; Zhengyan Lin; Wensheng Wang

doi:10.1007/s10959-005-7253-8

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

Younghoon Kim, Sungchul Lee, Zhengyan Lin, Wensheng Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	649-664
Number of pages	16
Journal	Journal of Theoretical Probability
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/s10959-005-7253-8
Publication status	Published - 2005 Jul

Bibliographical note

Funding Information:
1Department of Mathematics, Yonsei University, Seoul 120-749, Korea. 2Department of Mathematics, Zhejing University, Hangzhou 310028, China. 3Department of Statistics, East China Normal University, Shanghai 200062, China. E-mail: wswang@stat.ecnu.edu.cn 4To whom correspondence should be addressed. 5This work was supported by the BK21 project of the Department of Mathematics, Yon-sei University and Com2MaC in POSTECH. 6This work was supported by the BK21 project of the Department of Mathematics, Yon-sei University, the interdisciplinary research program of KOSEF 1999-2-103-001-5 and Com2MaC in POSTECH. 7This work was supported by NSFC (10401037) and 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/s10959-005-7253-8

Cite this

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abstract = "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.",

author = "Younghoon Kim and Sungchul Lee and Zhengyan Lin and Wensheng Wang",

note = "Funding Information: 1Department of Mathematics, Yonsei University, Seoul 120-749, Korea. 2Department of Mathematics, Zhejing University, Hangzhou 310028, China. 3Department of Statistics, East China Normal University, Shanghai 200062, China. E-mail: wswang@stat.ecnu.edu.cn 4To whom correspondence should be addressed. 5This work was supported by the BK21 project of the Department of Mathematics, Yon-sei University and Com2MaC in POSTECH. 6This work was supported by the BK21 project of the Department of Mathematics, Yon-sei University, the interdisciplinary research program of KOSEF 1999-2-103-001-5 and Com2MaC in POSTECH. 7This work was supported by NSFC (10401037) and the BK21 project of the Department of Mathematics, Yonsei University.",

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AU - Lee, Sungchul

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AU - Wang, Wensheng

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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.

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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