Asymmetric stochastic transport models with ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ symmetry

Abstract

By using the algebraic construction outlined in \cite{CGRS}, we introduce several Markov processes related to the ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ 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 Brownian Energy Process 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.

51 pages. arXiv admin note: text overlap with arXiv:1407.3367

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Cited by in corpus (14)

• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Orthogonal Dualities of Markov Processes and Unitary Symmetries
• Self-duality of Markov processes and intertwining functions
• ASEP(q,j) converges to the KPZ equation
• Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
• Local thermal equilibrium for certain stochastic models of heat transport
• Stochastic duality and eigenfunctions
• Orthogonal polynomial duality of a two-species asymmetric exclusion process
• Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes
• Totally asymmetric limit for models of heat conduction
• Local equilibrium in inhomogeneous stochastic models of heat transport
• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations
• Explicit Central Elements of $U_q(\mathfrak{gl}(N+1))$