PMID: 12786119Jun 6, 2003Paper

Directed random walks on directed percolation clusters

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Xiao-Hong WangS Havlin

Abstract

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.

References

Feb 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Z OlamiR Zeitak
Sep 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G HuberK Sneppen
Oct 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Z OlamiR Zeitak
May 18, 1987·Physical Review Letters·M Kardar, Y C Zhang

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