Asymmetric Stochastic Transport Models with Uq(su(1,1)) Symmetry

Journal article (2016)
Department
Delft Institute of Applied Mathematics (EEMCS) (TU Delft)
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Published Date

19-02-2016

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Source:

Journal of Statistical Physics, 163 (2), 2016

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Abstract

By using the algebraic construction outlined in Carinci et al. (arXiv:?1407.?3367, 2014), we introduce several Markov processes related to the Uq(su(1,1)) quantum Lie algebra. These processes serve as asymmetric transport models and their algebraic structure easily allows to deduce duality properties of the systems. The results include: (a) the asymmetric version of the Inclusion Process, which is self-dual; (b) the diffusion limit of this process, which is a natural asymmetric analogue of the and which turns out to have the Symmetric Inclusion Process as a dual process; (c) the asymmetric analogue of the KMP Process, which also turns out to have a symmetric dual process. We give applications of the various duality relations by computing exponential moments of the current.

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