Rates of convergence of means of Euclidean functionals
| dc.creator | Koo, Yooyoung | |
| dc.creator | Lee, Sungchul | |
| dc.date | 2006-09-14 | |
| dc.date | 2006-09-18 | |
| dc.date.accessioned | 2026-07-07T07:24:48Z | |
| dc.date.available | 2026-07-07T07:24:48Z | |
| dc.description | 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 (1994, 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 $EL(\{X_1,...,X_n\})/n^{(d-p)/d}$. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609382 | |
| dc.identifier | http://arxiv.org/abs/math/0609382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116508 | |
| dc.subject | Probability | |
| dc.subject | 60D05(Primary);05C80, 90C27(Secondary) | |
| dc.title | Rates of convergence of means of Euclidean functionals | |
| dc.type | text |