On dualities for SSEP and ASEP with open boundary conditions

Abstract

Duality relations for simple exclusion processes with general open boundaries are discussed. It is shown that a combination of spin operators and bosonic operators enables us to have an unified discussion for the duality relations with the open boundaries. As for the symmetric simple exclusion process (SSEP), more general results than previous studies are obtained; it is clarified that not only the absorbing sites, but also additional sites, called copying sites, are needed for the boundaries in the dual process for the SSEP. The role of the copying sites is to conserve information about the particle states on the boundary sites. The similar discussions are applied to the asymmetric simple exclusion process (ASEP), in which the q-analogues are employed, and it is clarified that the ASEP with open boundaries has a complicated dual process on the boundaries.

21 pages

References in corpus (4)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Duality and hidden symmetries in interacting particle systems
• A generalized Asymmetric Exclusion Process with $U_q({\mathfrak{sl}}_2)$ stochastic duality
• Duality relations for the ASEP conditioned on a low current

Cited by in corpus (7)

• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• Orthogonal Dualities of Markov Processes and Unitary Symmetries
• A reverse duality for the ASEP with open boundaries
• Stochastic Fusion of Interacting Particle Systems and Duality Functions
• Duality in stochastic processes from the viewpoint of basis expansions
• Markov duality and Bethe ansatz formula for half-line open ASEP
• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations