EXACT DISTRIBUTION FUNCTION FOR DISCRETE-TIME CORRELATED RANDOM-WALKSIN ONE-DIMENSION

A discrete time correlated random walk in one dimension is investigate d. Combinatorial arguments are used to calculate the exact probability distribution P-N(L), the probability that the correlated random walke r arrives at a distance L steps to the right of its starting point aft er exactly N steps. P-N(L) is calculated using arbitrary initial condi tions which permit the influence of end effects and boundary condition s to be calculated and several special cases are considered in detail. P-N(L) with arbitrary initial conditions is calculated both with and without a bias for motion in one direction yielding a useful model for the combined diffusion and drift of charged particles undergoing a co rrelated random walk in an applied field. The relation of the correlat ed random walk to the Ising model is also discussed. (C) 1998 American Institute of Physics. [S0021-9606(98)52140-X].