Points on $\operatorname{SO}(3)$ with low logarithmic energy
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912490206527488 |
|---|---|
| author | Beltrán, Carlos Carrasco, Federico Ferizović, Damir López-Gómez, Pedro R. |
| author_facet | Beltrán, Carlos Carrasco, Federico Ferizović, Damir López-Gómez, Pedro R. |
| contents | We describe several randomized collections of $3\times 3$ rotation matrices and analyze their associated logarithmic energy. The best one (i.e. the one attaining the lowest expected logarithmic energy) is constructed by choosing $r$ spherical points, which come from the zeros of a randomly chosen degree $r$ polynomial, and considering at each of these points a set of $s$ evenly distributed rotation matrices. This construction yields a new upper bound on the minimal logarithmic energy of $n=rs$ rotation matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Points on $\operatorname{SO}(3)$ with low logarithmic energy Beltrán, Carlos Carrasco, Federico Ferizović, Damir López-Gómez, Pedro R. Classical Analysis and ODEs 31C12, 60G55, Secondary: 31B15, 52C35 We describe several randomized collections of $3\times 3$ rotation matrices and analyze their associated logarithmic energy. The best one (i.e. the one attaining the lowest expected logarithmic energy) is constructed by choosing $r$ spherical points, which come from the zeros of a randomly chosen degree $r$ polynomial, and considering at each of these points a set of $s$ evenly distributed rotation matrices. This construction yields a new upper bound on the minimal logarithmic energy of $n=rs$ rotation matrices. |
| title | Points on $\operatorname{SO}(3)$ with low logarithmic energy |
| topic | Classical Analysis and ODEs 31C12, 60G55, Secondary: 31B15, 52C35 |
| url | https://arxiv.org/abs/2506.13388 |