Domany-Kinzel Model of Directed Percolation: Formulation as a Random-Walk Problem and Some Exact Results
- 22 March 1982
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 48 (12) , 775-778
- https://doi.org/10.1103/physrevlett.48.775
Abstract
It is shown that the directed percolation on certain two-dimensional lattices, in which the occupation probability is unity along one spatial direction, is related to a random-walk problem, and is therefore exactly solvable. As an example, the case of the triangular lattice is solved. It is also shown that the square-lattice solution obtained previously by Domany and Kinzel can be derived using Minkowski's "taxicab geometry."Keywords
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