NEW APPROACHES TO SHAPES OF ARBITRARY RANDOM-WALKS

The problem of the shape of a random object such as a flexible polymer chain was first tackled by Kuhn nearly thirty years after the answer to the probability distribution of its size was publicly sought for by Pearson in 1905. Since then, significant progress in the field has be en made, but the important task of evaluating both analytically and ac curately averaged individual principal components of the shape or iner tia tensor for a walk of a certain architectural type remains unfinish ed. We have recently developed a new and general formalism for both ex act and approximate calculations of these and other averages such as a sphericity and prolateness parameters, which is illustrated here for a n end-looped random walk and a self-avoiding or Edwards chain. We find that this combined open and closed random walk has surprisingly large r shape asymmetry than a simply open walk despite its smaller size.