q−Orthogonal dualities for asymmetric particle systems

We study a class of interacting particle systems with asymmetric interaction showing self-duality property. The includes the ASEP(q,θ), exclusion process, repulsive interaction, allowing up to θ∈N particles in each site, and ASIP(q,θ), θ∈R+, inclusion that is its attractive counterpart. extend setting investigation orthogonal duality properties done [8] for symmetric processes. analysis leads multivariate q−analogues Krawtchouk polynomials Meixner as functions generalized process version, respectively. also show how q-Krawtchouk orthogonality relations can be used compute exponential moments correlations ASEP(q,θ).