Site-bond representation and self-duality for totalistic probabilistic cellular automata

Details Site-bond representation and self-duality for totalistic probabilistic cellular automata Site-bond representation and self-duality for totalistic probabilistic cellular automata

2004-07-26

arxiv.org/abs/cond-mat/0407657v3

Journal of Statistical Mechanics: Theory and Experiment, P03002 (2005)

Physics

Condensed Matter

Statistical Mechanics

11 pages, minor corrections, journal reference added

Scientific paper

10.1088/1742-5468/2005/03/P03002

We study the one-dimensional two-state totalistic probabilistic cellular automata (TPCA) having an absorbing state with long-range interactions, which can be considered as a natural extension of the Domany-Kinzel model. We establish the conditions for existence of a site-bond representation and self-dual property. Moreover we present an expression of a set-to-set connectedness between two sets, a matrix expression for a condition of the self-duality, and a convergence theorem for the TPCA.

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