Abstract
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 language | English |
|---|---|
| Pages (from-to) | 4 |
| Number of pages | 1 |
| Journal | Physical Review E |
| Volume | 67 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2003 |