Real Space Renormalization-Group for Configurational Random Walk Models on a Hierarchical Lattice. The Asymptotic End-to-End Distance of a Weakly SARW in Dimension Four

We present a real space renormalization-group map for probabilities of random walks on a hierarchical lattice. From this, we study the asymptotic behavior of the end-to-end distance of a weakly self- avoiding random walk (SARW) that penalizes the (self-)intersection of two random walks in dimension four on the hierarchical lattice.