Directed random walks on directed percolation clusters.
The characteristics of directed random walks on directed percolation clusters are numerically studied. For two-dimensional clusters grown at the critical probability p(c), it is shown that the distance d of the directed random walkers from their most probable end point is determined by a probability distribution p(d) approximately d(-(1+w/nu)), where the values of w and nu are close to the values of the known exponents: w approximately 0.50 and nu approximately 0.63. This probability distribution is independent of the cluster's length t up to d values comparable to the cluster's width approximately t(nu). The results are shown to be consistent with a tree description of the directed percolation clusters.
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