  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.
