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.

18 pages

References in corpus (2)

• Particle hopping models and traffic flow theory
• Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions

Cited by in corpus (16)

• Metric properties of discrete time exclusion type processes in continuum
• Convergence to equilibrium in a class of interacting particle systems evolving in discrete time
• A slow-to-start traffic model related to a M/M/1 queue
• Ergodicity of some classes of cellular automata subject to noise
• Critical behavior of number-conserving cellular automata with nonlinear fundamental diagrams
• The Discrete-Time Facilitated Totally Asymmetric Simple Exclusion Process
• Self-organisation in cellular automata with coalescent particles: qualitative and quantitative approaches
• Approximating dynamics of a number-conserving cellular automaton by a finite-dimensional dynamical system
• Second order additive invariants in elementary cellular automata
• Stochastic stability of traffic maps
• Orbits of Bernoulli Measures in Cellular Automata
• Structure and dynamics in the low-density phase of a two-dimensional cellular automaton model of traffic flow
• Defect Particle Kinematics in One-Dimensional Cellular Automata
• On quasi successful couplings of Markov processes
• First-passage processes in a deterministic one-dimensional cellular automaton model of traffic flow
• Two-dimensional traffic rules and the density classification problem