Random walks with short memory in a disordered environment

The backward-jump model is investigated for the case of a bond-disordered lattice. The backward-jump model is a correlated nearest-neighbor random-walk model in which the walker has a different transition rate for jumps to its previously visited site than for jumps to all other nearest-neighbor sites. The standard formulation of the model must be modified if the disorder is introduced at the level of the usual master equation. The difficulties with the standard formulation are discussed in the paper. The first-order master equation for the disordered backward-jump model is established, and a symmetrized second-order equation that was suggested previously is derived from it.