A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting. (English) Zbl 07881350
The authors present a faster algorithm for direct sampling of random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of J. Cantarella et al. [J. Phys. A, Math. Theor. 49, No. 27, Article ID 275202, 9 p. (2016; Zbl 1342.82063)] which achieved a runtime of \(\Theta (n^{5/2})\) per sample, where \(n\) is the number of edges in the random equilateral closed polygon. The improved algorithm presented here improves the runtime to \(\Theta (n^{2})\) per sample, The authors use the new sampling method to investigate the probability of finding unknots among equilateral closed polygons cover covering a polygonal length from \(n = 16\) to \(n = 3043\). The authors detect the unknot by computing invariants based on the Alexander polynomial.
Reviewer: Claus Ernst (Bowling Green)
MSC:
| 57K10 | Knot theory |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 82D60 | Statistical mechanics of polymers |
| 60G50 | Sums of independent random variables; random walks |
Citations:
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