Open Access
January, 1994 Survival of One-Dimensional Cellular Automata Under Random Perturbations
Maury Bramson, Claudia Neuhauser
Ann. Probab. 22(1): 244-263 (January, 1994). DOI: 10.1214/aop/1176988858

Abstract

Cellular automata have been the subject of considerable recent study in the statistical physics literature, where they provide examples of easily accessible nonlinear phenomena. We investigate a class of nearest neighbor cellular automata taking values $\{0,1\}$ on $\mathbb{Z}$. In the deterministic setting, this class includes rules which yield fractal-like patterns when starting from a single occupied site. We are interested here in the asymptotic behavior of systems subjected to small random perturbations. In this context, one wishes to ascertain under which conditions such systems survive with positive probability. We show here that, except in trivial cases, these systems in fact always survive, and they possess densities which remain bounded away from 0.

Citation

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Maury Bramson. Claudia Neuhauser. "Survival of One-Dimensional Cellular Automata Under Random Perturbations." Ann. Probab. 22 (1) 244 - 263, January, 1994. https://doi.org/10.1214/aop/1176988858

Information

Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0793.60107
MathSciNet: MR1258876
Digital Object Identifier: 10.1214/aop/1176988858

Subjects:
Primary: 60K35
Secondary: 82C20

Keywords: cellular automata , Random perturbations , rescaling , survival

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.22 • No. 1 • January, 1994
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