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2021 qOrthogonal dualities for asymmetric particle systems
Gioia Carinci, Chiara Franceschini, Wolter Groenevelt
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Electron. J. Probab. 26: 1-38 (2021). DOI: 10.1214/21-EJP663


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 θN particles in each site, and the ASIP(q,θ), θR+, 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 qanalogues 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).

Funding Statement

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.


Download Citation

Gioia Carinci. Chiara Franceschini. Wolter Groenevelt. "qOrthogonal dualities for asymmetric particle systems." Electron. J. Probab. 26 1 - 38, 2021.


Received: 26 March 2020; Accepted: 7 June 2021; Published: 2021
First available in Project Euclid: 20 July 2021

Digital Object Identifier: 10.1214/21-EJP663

Primary: 60J27, 60K35, 81R05, 81R10


Vol.26 • 2021
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