Probability of Initial Ring Closure in the Restricted Random-Walk Model of a Macromolecule

The probability of initial ring closure in the restricted random-walk model of a macromolecule is investigated. From a study of the known exact numbers of polygons on the simple quadratic lattice up to 18 sides and on the triangular lattice up to 16 sides, it is concluded that the probability of initial ring closure in two-dimensions of large ring size k varies inversely as k1.83—θ, where 0≤θ≤0.05, and this is significantly higher than the dependence on the inverse square of k found by Wall's statistical investigation. It is found that the mean area of initial ring closures in a plane varies as k32.