Combinatorics of a disordered two-species ASEP on a torus

We define a new disordered asymmetric simple exclusion process (ASEP) with two species of particles, first-class particles labelled $\bullet$ and second-class ${\scriptstyle \Box}$, on two-dimensional toroidal lattice. The dynamics is controlled by $\bullet$, which only move horizontally, forward backward hopping rates $p_i$ $q_i$ respectively if the row $i$. motion \Box}$ depends relative position these respect to $\bullet$'s, can be both horizontal vertical. show that stationary weight any configuration proportional monomial in $p_i$'s $q_i$'s. Our projects ASEP ring, so explains combinatorially distribution latter first derived Evans (Europhysics Letters, 1996). compute partition function, as well densities currents $\bullet$'s \Box}$'s state. observe novel mechanism we call Scott Russell phenomenon: current vertical direction same direction.