Ergodicity of cellular automata subject to noise

A major challenge in the implementation of massively parallel computing structures at the nano-level is the inevitability of thermal noise.  Cellular automata (CA) provide a convenient mathematical framework to address this challenge at the fundamental level. Constructing a deterministic CA whose trajectories remain distinguishable under the influence of noise is a notoriously difficult problem.  Most CA appear to be highly unstable against noise and forget their initial conditions under the slightest positive noise.  This is manifested as the ergodicity of the associated Markov process.  Nevertheless, the mechanism responsible for this forgetfulness can be quite different from one CA to another, depending crucially on the dynamical and combinatorial properties of the system. I will discuss some recent results regarding the ergodicity of CA subject to noise.  I will then focus on one of these results whose proof is based on the notion of entropy.  This is joint work with Irène Marcovici and Mathieu Sablik