A generalized asymmetric exclusion process with Uq(sl2) stochastic duality

G Carinci, C Giardinà, FHJ Redig, T Sasamoto

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Abstract

We study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by q ∈ (0, 1) and where at most 2 j ∈ N particles per site are allowed. The process is constructed from a (2 j + 1)-dimensional representation of a quantum Hamiltonian with Uq (sl2) invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP(q, j ), we prove self-duality with several selfduality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the first q-exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from a homogeneous product measure.
Original languageEnglish
Pages (from-to)1-47
Number of pages47
JournalProbability Theory and Related Fields
DOIs
Publication statusPublished - 2015

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