Random Flight with Multiple Partial Correlations

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Abstract
The fundamental statistical properties of a linear polymer can be best studied by a more general model of random flight with multiple partial correlations. Results show that the problems of free rotation and symmetrically restricted rotation in polymers correspond to one and two partial correlations, respectively. The present study of the correlation function by means of difference equations enables one to carry out the generalization to higher orders of partial correlations. The mean square value of the distance r between the ends of the chain is studied for both finite and infinite number of links, and for multiple partial correlations. It is shown that the case of one partial correlation corresponds to a Markoff chain, and the distribution of r is found to be normal.