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

Journal article (2015)
Department
Delft Institute of Applied Mathematics (EEMCS) (TU Delft)
Copyright: This article is published with open access at Springerlink.com
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Published Date

05-11-2015

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Source:

Probability Theory and Related Fields, 2015

ISSN:

0178-8051

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

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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