Dynamical pair approximation for cellular automata with shuffle update

The random shuffle update method for the asymmetric exclusion process (ASEP) is introduced, and the dynamical pair technique is extended in order to analyse its dynamics. A sequence of approximate models is introduced, the first element of which corresponds to the classical parallel update rule whose pair dynamics is reviewed. It is then shown how the argument may be extended inductively to solve for the two-cell configuration probabilities for each element of the sequence of approximate models. A formal limit is then taken, and macroscopic velocities and flow rates are derived.