Abstract
Different approaches to the self-avoiding walk problem are reviewed. The problem first arose in the statistical physics of linear polymers in connection with the evaluation of the average size of a polymer. The probability distribution density WN(R) for the vector R connecting the end-points of an N-step self-avoiding walk is the main quantity in this problem. The equation for WN(R) seems to be invariant under the scaling transformation group. This means that the renormalization group method can be used to determine the asymptotic form of WN(R) as
N → ∞
.