A The Random Walk Problem

The conformation of a macromolecule consisting of N independent subchains (or segments) can be considered as the result of a random walk of a Brownian particle after N independent steps (Flory 1953). 

One can assume that the displacement r of the particle is random and a probability distribution function 

Since the space is isotropic, we consider the distribution function to be a spherically symmetrical one, so that 

The situation can be simplified by proposing that the one-step displacement is constant and equal to 6, so that the probability distribution function takes the form 

It is easy to see that the function is normalised to unity and the mean square displacement is equal to b2. Indeed 

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