Self-Duality for the Two-Component Asymmetric Simple Exclusion Process

Abstract

We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra $U_q[{\mathfrak{gl}}_3]$. We construct all invariant measures in explicit form and discuss some of their properties. We also prove a sum rule for the duality functions.

27 pages

References in corpus (3)

• Duality and hidden symmetries in interacting particle systems
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Determinant representation for some transition probabilities in the TASEP with second class particles

Cited by in corpus (16)

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• Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Self-duality of Markov processes and intertwining functions
• A reverse duality for the ASEP with open boundaries
• Quantum algebra symmetry of the ASEP with second-class particles
• Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
• Uphill in reaction-diffusion multi-species interacting particles systems
• Limiting current distribution for a two species asymmetric exclusion process
• Regularity comparison of symbolic powers, integral closure of powers and powers of edge ideals
• Duality relations for the ASEP conditioned on a low current
• Orthogonal polynomial duality of a two-species asymmetric exclusion process
• Q-zero range has random walking shocks