## The Annals of Probability

### Survival of One-Dimensional Cellular Automata Under Random Perturbations

#### 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

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