Exact stationary state for an asymmetric exclusion process with fully parallel dynamics

The exact stationary state of an asymmetric exclusion process with fully pa rallel dynamics is obtained using the matrix product ansatz. We give a simp le derivation for the deterministic case by a physical interpretation of th e dimension of the matrices. We prove the stationarity via a cancellation m echanism, and by making use of an explicit representation of the matrix alg ebra we easily find closed expressions for the correlation functions in the general probabilistic case. Asymptotic expressions, obtained by making use of earlier results, allow us to derive the exact phase diagram. [S1063-651 X(99)03205-5].