Stationary blocking measures for one-dimensional nonzero mean exclusion processes

The product Bernoulli measures ρα with densities α, α ∈ [0, 1], are the extremal translation invariant stationary measures for an exclusion process with irreducible random walk kernel p(·). In d = 1, stationary measures that are not translation invariant are known to exist for specific p(·) satisfying σ_x xp(x) > 0. These measures are concentrated on configurations that are completely occupied by particles far enough to the right and are completely empty far enough to the left; that is, they are blocking measures. Here, we show stationary blocking measures exist for all exclusion processes in d = 1, with p(·) having finite range and σ_x xp(x) > 0.