The Annals of Probability

Survival of One-Dimensional Cellular Automata Under Random Perturbations

Maury Bramson and Claudia Neuhauser

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 244-263.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988858

Digital Object Identifier
doi:10.1214/aop/1176988858

Mathematical Reviews number (MathSciNet)
MR1258876

Zentralblatt MATH identifier
0793.60107

JSTOR
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

Keywords
Cellular automata random perturbations survival rescaling

Citation

Bramson, Maury; Neuhauser, Claudia. Survival of One-Dimensional Cellular Automata Under Random Perturbations. Ann. Probab. 22 (1994), no. 1, 244--263. doi:10.1214/aop/1176988858. https://projecteuclid.org/euclid.aop/1176988858


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