Asymptotics of Best-Packing on Rectifiable Sets
| dc.creator | Borodachov, S. V. | |
| dc.creator | Hardin, D. P. | |
| dc.creator | Saff, E. B. | |
| dc.date | 2006-05-05 | |
| dc.date.accessioned | 2026-07-07T07:13:43Z | |
| dc.date.available | 2026-07-07T07:13:43Z | |
| dc.description | We investigate the asymptotic behavior, as $N$ grows, of the largest minimal pairwise distance of $N$ points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurations. For this purpose, we compare best-packing configurations with minimal Riesz $s$-energy configurations and determine the $s$-th root asymptotic behavior (as $s\to \infty)$ of the minimal energy constants. We show that the upper and the lower dimension of a set defined through the Riesz energy or best-packing coincides with the upper and lower Minkowski dimension, respectively. For certain sets in ${\rm {\bf R}}^d$ of integer Hausdorff dimension, we show that the limiting behavior of the best-packing distance as well as the minimal $s$-energy for large $s$ is different for different subsequences of the cardinalities of the configurations. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0605021 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0605021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112576 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 11K41, 70F10, 28A78 | |
| dc.title | Asymptotics of Best-Packing on Rectifiable Sets | |
| dc.type | text |