The `true' self-avoiding walk with bond repulsion is 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)}. First we prove a limit theorem for the distribution of the local time process of this walk. Using this result, later we prove a limit theorem for the late time distribution of the position of the random walker, with scaling proportional to the 2/3-th power of time. As a by-product we also obtain an apparently new identity related to Brownian excursions and Bessel bridges.
Key words: self-repelling random walk, local time, limit theorems, anomalous diffusion