Q−orthogonal dualities for asymmetric particle systems

Gioia Carinci, Chiara Franceschini, Wolter Groenevelt

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
10 Downloads (Pure)


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).

Original languageEnglish
Article number108
Pages (from-to)1-38
Number of pages38
JournalElectronic Journal of Probability
Publication statusPublished - 2021


  • Asymmetric interacting particle systems
  • Q-orthogonal polynomials
  • Quantum algebras
  • Self-duality


Dive into the research topics of 'Q−orthogonal dualities for asymmetric particle systems'. Together they form a unique fingerprint.

Cite this