A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting

Autor:	Cantarella, Jason, Schumacher, Henrik, Shonkwiler, Clayton
Rok vydání:	2023
Předmět:	Condensed Matter - Statistical Mechanics Mathematics - Probability Mathematics - Symplectic Geometry 60D05 53D30 82D60
Druh dokumentu:	Working Paper
Popis:	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. Comment: 12 pages, 4 figures. This version includes a table of estimated unknot probabilities for equilateral polygons from 16 to 3043 edges, and an additional data file "unknot-inverse-samples.tsv" giving the raw data from our experiment
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.10163 Zobrazit plný text záznamu View this record from Arxiv