Invariant Measures and Convergence for Cellular Automaton 184 and Related Processes

Abstract

For a class of one-dimensional cellular automata, we review and complete the characterization of the invariant measures (in particular, all invariant phase separation measures), the rate of convergence to equilibrium, and the derivation of the hydrodynamic limit. The most widely known representatives of this class of automata are: Automaton 184 from the classification of S. Wolfram, an annihilating particle system and a surface growth model.