A reverse duality for the ASEP with open boundaries

Abstract

We prove a duality between the asymmetric simple exclusion process (ASEP) with non-conservative open boundary conditions and an asymmetric exclusion process with particle-dependent hopping rates and conservative reflecting boundaries. This is a reverse duality in the sense that the duality function relates the measures of the dual processes rather than expectations. Specifically, for a certain parameter manifold of the boundary parameters of the open ASEP this duality expresses the time evolution of a family of shock product measures with $N$ microscopic shocks in terms of the time evolution of $N$ particles in the dual process. The reverse duality also elucidates some so far poorly understood properties of the stationary matrix product measures of the open ASEP given by finite-dimensional matrices.

40 pages

References in corpus (7)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Duality and hidden symmetries in interacting particle systems
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• Matrix Product Steady States as Superposition of Product Shock Measures in 1D Driven Systems
• Temporal evolution of product shock measures in TASEP with sublattice-parallel update

Cited by in corpus (9)

• Approximating the stationary distribution of the ASEP with open boundaries
• Markov duality and Bethe ansatz formula for half-line open ASEP
• Askey-Wilson signed measures and open ASEP in the shock region
• A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
• Mixing times and cutoff for the TASEP in the high and low density phase
• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations
• Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems
• The steady state of the boundary-driven multiparticle asymmetric diffusion model
• Correlations of density and current fluctuations in single-file motion of hard spheres and in driven lattice gas with nearest-neighbor interaction