AUTOCORRELATION FUNCTIONS FOR DISCRETE RANDOM-WALKS ON DISORDERED LATTICE

We propose the structure of leading and correction terms in the mean end-to-end displacement and autocorrelation functions for the blind and myopic ant random walks in disordered lattices. The essential difference between the blind and myopic ants is that the blind ant can remain at a site for multiple time steps whereas the mypoic ant must always move. This structure incorporates the regular oscillations recently found in certain autocorrelation functions of myopic ant random walks on several disordered substrates. Some predictions of the proposed structure are confirmed on two- and three-dimensional lattices at the percolation threshold, using a numerical technique that performs the exact summation of all Brownian paths starting from all points of any given finite cluster on a lattice. © 1990 The American Physical Society.