Journal
PROBABILITY THEORY AND RELATED FIELDS
Volume 166, Issue 3-4, Pages 887-933Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-015-0674-0
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Funding
- FIRB [RBFR10N90W]
- National Group of Mathematical Physics (GNFM-INdAM)
- KAKENHI [22740054]
- Sumitomo Foundation
- INFN
- Grants-in-Aid for Scientific Research [25103004, 26610019, 22740054] Funding Source: KAKEN
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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 and where at most particles per site are allowed. The process is constructed from a -dimensional representation of a quantum Hamiltonian with 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 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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