We consider a nearest neighbour random walk on Z, for which the probability of jumping along a bond of the lattice is proportional to exp{-g (number of previous jumps along that bond)^k}, with g and k fixed positive parameters. After a review of earlier results obtained for the case k = 1 we outline the generalizations for 0 < k < 1, obtaining a whole range of anomalous diffusion limits: at late times the position of the random walker scales with the (k+1)/(k+2)-th power of the number of steps.
Key words: self-repelling random walk, local time, limit theorems, anomalous diffusion