‘True’ self-avoiding walks with generalized bond repulsion on ℤ

Abstract

We consider a nearest-neighbor 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 ], withg>0,k∈(0,1]. After a review of earlier results obtained for the casek=1 we outline the generalizations fork∈(0,1), obtaining a whole range of anomalous diffusion limits.