Q−orthogonal dualities for asymmetric particle systems

Gioia Carinci, Chiara Franceschini, Wolter Groenevelt

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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).

Original languageEnglish
Article number108
Pages (from-to)1-38
Number of pages38
JournalElectronic Journal of Probability
Volume26
DOIs
Publication statusPublished - 2021

Keywords

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

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