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

Abstract

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.

15 pages, 9 figures, submited to PRE

References in corpus (5)

• Quasi-stationary distributions for stochastic processes with an absorbing state
• Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
• Numerical analysis of the master equation
• Growth Exponent in the Domany-Kinzel Cellular Automaton
• Scaling Exponents of Rough Surfaces Generated by the Domany-Kinzel Cellular Automaton

Cited by in corpus (3)

• Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics
• Quasi-Stationary Distributions for Models of Heterogeneous Catalysis
• Generalization of Fluctuation-Dissipation Theorem to Systems with Absorbing States