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 language | English |
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Article number | 108 |
Pages (from-to) | 1-38 |
Number of pages | 38 |
Journal | Electronic Journal of Probability |
Volume | 26 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Asymmetric interacting particle systems
- Q-orthogonal polynomials
- Quantum algebras
- Self-duality