Journal of Statistical Physics, VoL 30, No. 2, 1983. p. 509-518.
The diffusion of many particles on a lattice is an example of a correlated random-walk process. Recently the waiting-time distributions for two consecutive jumps of a tagged particle have been determined numerically and the time-dependent correlations analyzed in detail. The information over these two consecutive jumps is used to determine the position and velocity autocorrelation functions, and very satisfactory results are obtained for three-dimensional lattices. However, the information of the two consecutive jumps is insufficient when the jump rate of the tagged particle is large compared to that of the other particles, and this approximation fails completely in one dimension. For the linear chain, another approximation which accounts for correlations over all jumps is compared with the numerical simulations.