Random walks over polymer chains, modelled as simple random walks or self-avoiding walks, were considered. Each polymer was permitted to jump to any Euclidean, but not necessarily chemical, neighboring site. For frozen chain configurations, the distribution of walker displacements along the chain exhibited a paradoxical behavior. The width of the displacement distribution (inter-quartile distance) increased with the square root of time, but the distributions had long power-law tails. In the case of annealed configurations, the displacement distribution was Lévy-like and its width was strongly super-diffusive.

I.M.Sokolov, J.Mai, A.Blumen: Physical Review Letters, 1997, 79[5], 857-60