The probability of initial ring closure in the restricted randomhyphen;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 twohyphen;dimensions of large ring sizekvaries inversely ask1.83mdash;thgr;, where 0le;thgr;le;0.05, and this is significantly higher than the dependence on the inverse square ofkfound by Wall's statistical investigation. It is found that the mean area of initial ring closures in a plane varies ask32.
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