Directed random walks on directed percolation clusters

Xiao Hong Wang, Ehud Perlsman, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The characteristics of directed random walks on directed percolation clusters are numerically studied. For two-dimensional clusters grown at the critical probability [Formula presented] it is shown that the distance d of the directed random walkers from their most probable end point is determined by a probability distribution [Formula presented] where the values of w and [Formula presented] are close to the values of the known exponents: [Formula presented] and [Formula presented] This probability distribution is independent of the cluster’s length t up to d values comparable to the cluster’s width [Formula presented] The results are shown to be consistent with a tree description of the directed percolation clusters.

Original languageEnglish
Pages (from-to)4
Number of pages1
JournalPhysical Review E
Issue number5
StatePublished - 2003


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