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