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

Younghoon Kim, Sungchul Lee, Zhengyan Lin, Wensheng Wang

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)649-664
Number of pages16
JournalJournal of Theoretical Probability
Volume18
Issue number3
DOIs
Publication statusPublished - 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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