Our model consists of two parts. First we have the basic chain, and secondly we have the tube and its motion. So:
The Gaussian character of the distribution of primitive chain conformations is consistent with the reptation pictured in Fig. (8.2). The chain continuously creates new pieces of tube, which may be chosen in random directions with step length a. Then is a Gaussian vector.
Apparently we have introduced two new parameters, the contour length L and the step length a. Only one of them however is independent, because they are related by , where the first equality stems from the fact that we are dealing with a Rouse chain, and the second equality follows from an application of Eq. (8.1).