Direct Sampling of Confined Polygons in Linear Time
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_ | 1866918504735703040 |
|---|---|
| author | Shonkwiler, Clayton Theis, Kandin |
| author_facet | Shonkwiler, Clayton Theis, Kandin |
| contents | We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry, sampling such polygons reduces to sampling a moment polytope, and in our confinement model this polytope turns out to be very natural from a combinatorial point of view. This connection to combinatorics yields both our fast sampling algorithm and explicit formulas for the expected distances of vertices to the origin. We use our algorithm to investigate the expected total curvature of confined polygons, leading to a very precise conjecture for the asymptotics of total curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Direct Sampling of Confined Polygons in Linear Time Shonkwiler, Clayton Theis, Kandin Geometric Topology Statistical Mechanics Computational Geometry Symplectic Geometry 57K10, 53A04, 53D30, 82D60, 05A05 We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry, sampling such polygons reduces to sampling a moment polytope, and in our confinement model this polytope turns out to be very natural from a combinatorial point of view. This connection to combinatorics yields both our fast sampling algorithm and explicit formulas for the expected distances of vertices to the origin. We use our algorithm to investigate the expected total curvature of confined polygons, leading to a very precise conjecture for the asymptotics of total curvature. |
| title | Direct Sampling of Confined Polygons in Linear Time |
| topic | Geometric Topology Statistical Mechanics Computational Geometry Symplectic Geometry 57K10, 53A04, 53D30, 82D60, 05A05 |
| url | https://arxiv.org/abs/2501.04885 |