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Journal article (2015)

Authors

G. Carinci Applied Probability - EEMCS
C Giardinà External organisation
F.H.J. Redig Applied Probability - EEMCS
Tomohiro Sasamoto External organisation
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2015 G. Carinci, C Giardinà, F.H.J. Redig, T Sasamoto
DOI: https://doi.org/10.1007/s00440-015-0674-0
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Published Date

2015

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.

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