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

Norio Konno·Xia Ma
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Abstract

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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Norio Konno, Xia Ma. 2005-06-11. Site-bond representation and self-duality for totalistic probabilistic cellular automata. https://doi.org/10.1088/1742-5468%2F2005%2F03%2Fp03002

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