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.
Bibliographical noteFunding 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: email@example.com 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
- Statistics, Probability and Uncertainty