Abstract
The case of a random walk on a one-dimensional inhomogeneous lattice is considered when the rate constants of the particle jumping to adjacent lattice points depend on the particle's position and jumping direction. The macroscopic characteristics of the process are evaluated for the lattice length tending to infinity. The requirements to be met by the sequences of jumping rate constants for the process to be self-averaging are analysed. In this case the macroscopic characteristics are shown to be equivalent to those of the random walk on a homogeneous lattice with an effective jumping rate constant. A method has been found for computing the effective jumping rate constant for a large class of inhomogeneous lattices.