Rates of Convergence of Means of Euclidean Functionals |
| |
Authors: | Yooyoung Koo Sungchul Lee |
| |
Affiliation: | (1) Department of Mathematics, Sungkyunkwan University, Suwon, Korea, 440-746;(2) Department of Mathematics, Yonsei University, Seoul, Korea, 120-749 |
| |
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,…,X
n
} from 0,1]
d
, L({X
1,…,X
n
})/n
(d−p)/d
converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X
1,…,X
n
})/n
(d−p)/d
.
Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University.
S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University. |
| |
Keywords: | Rate of convergence Minimal matching Minimal spanning tree Traveling salesman problem |
本文献已被 SpringerLink 等数据库收录! |
|