Renormalization-group method in the self-avoiding random walk problem

Renormalization-group equations are obtained for the transformed distribution of the probability density for the vector $\mathbf r$ joining the ends of the paths of a particle in a self-avoiding random walk in $n$-dimensional Euclidean space. The asymptotic behavior of the probability density is calculated for the case $4-n\ll 1$ when the number $N$ of individual displacements of the particle tends to infinity.