TY - JOUR

T1 - A generalized asymmetric exclusion process
with Uq(sl2) stochastic duality

AU - Carinci, G

AU - Giardinà, C

AU - Redig, FHJ

AU - Sasamoto, T

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://resolver.tudelft.nl/uuid:603e9149-cef0-4224-84c2-f588ae5050f7

U2 - 10.1007/s00440-015-0674-0

DO - 10.1007/s00440-015-0674-0

M3 - Article

SP - 1

EP - 47

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

ER -