Q−orthogonal dualities for asymmetric particle systems

Carinci, G.; Franceschini, Chiara; Groenevelt, W.G.M.

doi:10.1214/21-EJP663

Q−orthogonal dualities for asymmetric particle systems

Title

Q−orthogonal dualities for asymmetric particle systems

Author

Carinci, G. (Università di Modena e Reggio Emilia)
Franceschini, Chiara (Lisbon Technical University)
Groenevelt, W.G.M. (TU Delft Analysis)

Date

2021

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).

Subject

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

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http://resolver.tudelft.nl/uuid:76b4a9b8-b1e7-4c74-98de-1e18d1243715

DOI

https://doi.org/10.1214/21-EJP663

ISSN

1083-6489

Source

Electronic Journal of Probability, 26, 1-38

Part of collection

Institutional Repository