A CONTINUUM GAMBLERS RUIN MODEL

A continuum version of the gambler's ruin model is presented. The following functions are derived: end-to-end vector distributions of both loops and ties and their Fourier transforms, chain length distributions of both loops and ties, and their Laplace transforms. A few of the lower moments of these distributions are also calculated. Gambler's ruin models lack sufficient detail to accurately predict the degree of adjacent reentry but nevertheless predict that most chains return to the crystal very near the point of departure. For example, on the basis of this model, we predict that 3/4 of the chains in polyethylene return to the same crystallite within about 14 .