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).

Q−orthogonal dualities for asymmetric particle systems / Carinci, G.; Franceschini, C.; Groenevelt, W.. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 26:none(2021), pp. 1-38. [10.1214/21-EJP663]

Q−orthogonal dualities for asymmetric particle systems

Carinci G.;Franceschini C.;Groenevelt W.
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).
2021
26
none
1
38
Q−orthogonal dualities for asymmetric particle systems / Carinci, G.; Franceschini, C.; Groenevelt, W.. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 26:none(2021), pp. 1-38. [10.1214/21-EJP663]
Carinci, G.; Franceschini, C.; Groenevelt, W.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1257340
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