A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler · Journal of Physics A Mathematical and Theoretical · 2024
Abstract 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 et al (2016 J. Phys. A: Math. Theor. 49 275202) 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.