We have investigated the random walk of particles in the frame of a conventional master equation for directed random walks. The transfer rates are supposed to be random variables and we incorporate the possibility of correlations. We assume that the chain consists of successive segments of random lengths. Within a given segment, the transfer rates are equal to a single random variable. The transfer rates belonging to two different segments are supposed to be independent and distributed according to the same probability law. We have calculated the time-asymptotic behavior of the mean coordinate of the particle. The resulting character of the motion emerges from the interplay between two basic features: the probability of having a small value of the transfer rate and the probability of having long segments. If the first moment of the segment-length distribution diverges, the asymptotic regime undergoes radical changes as compared to the noncorrelated model.

• Received 11 May 1992

DOI:https://doi.org/10.1103/PhysRevE.47.1610