Ergodicity conjecture for additive one-dimensional nearest-neighbor interacting particle systems

Let an additive interacting particle system (IPS) evolve on a one-dimensional lattice with homogeneous, one-sided, nearest-neighbor interaction and positive rates. Additive ergodicity conjecture. Every such IPS is ergodic. The paper describes this as the affirmative symmetric subcase investigated by Toom et al. and states that it proves the claim, so this special case is no longer open.