We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(), asymmetric exclusion process, with a repulsive interaction, allowing up to particles in each site, and the ASIP, , asymmetric inclusion process, that is its attractive counterpart. We extend to the asymmetric setting the investigation of orthogonal duality properties done in  for symmetric processes. The analysis leads to multivariate 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().
C.F. acknowledges support from the European Research Council (ERC) under the European Union Horizon 2020 research and innovative program (grant agreement No 715734). We also thank the referees for their helpful comments which helped improving the quality of the manuscript.
The authors thank Cristian Giardinà and Frank Redig for useful discussion.
"Orthogonal dualities for asymmetric particle systems." Electron. J. Probab. 26 1 - 38, 2021. https://doi.org/10.1214/21-EJP663