A random cellular automaton related to the noisy Burgers equation

We derive a random cellular automaton (CA) model from the noisy Burgers equation. The method for that derivation is a nonanalytic limiting procedure called ‘ultra-discretization method’ (UDM) proposed by Tokihiro et al. (Phys. Rev. Lett. 76 (1996) 3247). Special attention is paid to the noise term. It is the intention of this paper to propose a random CA model which could be used as a starting point to understand on a CA basis the precise mechanism leading from deterministic evolutionary equations which trigger chaos such as the Kuramoto–Shivashinsky (KS) equation to equivalent stochastic large-scale descriptions. We investigate our CA model to ensure that it belongs to the same universality class as the noisy Burgers (and thereby also KS) equation itself.