The knot probability of semiflexible polygons on the cubic lattice is investigated. The degree of stiffness of the polygon is mimicked by introducing a bending fugacity conjugate to the curvature of the polygon. By generalizing Kesten's pattern theorem to semiflexible walks, we show that for any finite value of the bending fugacity all except exponentially few sufficiently long polygons are knotted.
Knotted polygons with curvature in Z(3)
ORLANDINI, ENZO;
1998
Abstract
The knot probability of semiflexible polygons on the cubic lattice is investigated. The degree of stiffness of the polygon is mimicked by introducing a bending fugacity conjugate to the curvature of the polygon. By generalizing Kesten's pattern theorem to semiflexible walks, we show that for any finite value of the bending fugacity all except exponentially few sufficiently long polygons are knotted.
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