Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

Details Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

2002-07-10

arxiv.org/abs/cond-mat/0207264v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 9 figures, submited to PRE

Scientific paper

10.1103/PhysRevE.66.046135

We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and two-site levels. We characterize the distribuitions by their mean, and various moment ratios, and analyze the lifetime of the QS state, and the relaxation time to attain this state. Of particular interest are the scaling properties of the QS state along the critical line separating the active and absorbing phases. These exhibit a high degree of similarity to the contact process and the Malthus-Verhulst process (the closest continuous-time analogs of the DKCA), which extends to the scaling form of the QS distribution.

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