On knots in a model for the adsorption of ring polymers

Abstract

The occurence of knots in a model of a ring polymer interacting with a surface is considered. The polymer is described by a self-avoiding polygon (SAP) and interacts with the surface through a short-range interaction. It is proven rigorously that, for all non-zero temperatures, all except exponentially few SAPs contain a knot. We also show that the average knot complexity grows at least linearly with the length of the polymer, for sufficiently long polymers.