A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915313324392448 |
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| author | Cantarella, Jason Schumacher, Henrik Shonkwiler, Clayton |
| author_facet | Cantarella, Jason Schumacher, Henrik Shonkwiler, Clayton |
| contents | We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of Cantarella, Duplantier, Shonkwiler, and Uehara (2016) and has (expected) time per sample quadratic in the number of edges in the polygon. We use our new sampling method and a new code for computing invariants based on the Alexander polynomial to investigate the probability of finding unknots among equilateral closed polygons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting Cantarella, Jason Schumacher, Henrik Shonkwiler, Clayton Statistical Mechanics Probability Symplectic Geometry 60D05, 53D30, 82D60 We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of Cantarella, Duplantier, Shonkwiler, and Uehara (2016) and has (expected) time per sample quadratic in the number of edges in the polygon. We use our new sampling method and a new code for computing invariants based on the Alexander polynomial to investigate the probability of finding unknots among equilateral closed polygons. |
| title | A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting |
| topic | Statistical Mechanics Probability Symplectic Geometry 60D05, 53D30, 82D60 |
| url | https://arxiv.org/abs/2309.10163 |