Probability Distribution of the Radius of Gyration of a Flexible Polymer

Abstract

Various aspects of the mathematics of the probability distribution PN(Sx) of one component of the square of the radius of gyration of an ideal Brownian chain with N units are presented. A rigorous expression for PN(Sx) in the form of a contour integral is obtained. The resulting integral is written in terms of Tchebichef polynomials. Several rigorous and approximate results are obtained for both the limiting distribution (N infinite) and for finite N.