Scaling Conjecture Regarding the Number of Unknots among Polygons of <i>N</i>≫1 Edges

Abstract

The conjecture is made based on a plausible, but not rigorous argument, suggesting that the unknot probability for a randomly generated self-avoiding polygon of N≫1 edges has only logarithmic, and not power law corrections to the known leading exponential law: Punknot(N)∼exp−N/N0+o(lnN) with N0 being referred to as the random knotting length. This conjecture is consistent with the numerical result of 2010 by Baiesi, Orlandini, and Stella.

Keywords

• polymers
• knots
• unknot probability