Site-bond representation and self-duality for totalistic probabilistic cellular automata
Statistical Mechanics
2009-11-10 v3
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.
Cite
@article{arxiv.cond-mat/0407657,
title = {Site-bond representation and self-duality for totalistic probabilistic cellular automata},
author = {Norio Konno and Xia Ma},
journal= {arXiv preprint arXiv:cond-mat/0407657},
year = {2009}
}
Comments
11 pages, minor corrections, journal reference added