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A generalized Asymmetric Exclusion Process with Uq(sl2) stochastic duality
, 2014
"... We study a new process, which we call ASEP(q, j), where particles move asymmet-rically on a one-dimensional integer lattice with a bias determined by q ∈ (0, 1) and where at most 2j ∈ N particles per site are allowed. The process is constructed from a (2j+1)-dimensional representation of a quantum H ..."
Abstract
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We study a new process, which we call ASEP(q, j), where particles move asymmet-rically on a one-dimensional integer lattice with a bias determined by q ∈ (0, 1) and where at most 2j ∈ N particles per site are allowed. The process is constructed from a (2j+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 self-duality 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 con-ditions (both a shock or a rarefaction fan) as well as when the process is started from an homogeneous product measure.
