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 (Formula presented.) and where at most (Formula presented.) particles per site are allowed. The process is constructed from a (Formula presented.)-dimensional representation of a quantum Hamiltonian with (Formula presented.) 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.

A generalized asymmetric exclusion process with Uq(sl2) stochastic duality / Carinci, Gioia; Giardina', Cristian; Redig, Frank; Sasamoto, Tomohiro. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - 166:3(2016), pp. 887-933. [10.1007/s00440-015-0674-0]

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

CARINCI, GIOIA;GIARDINA', Cristian;
2016

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 (Formula presented.) and where at most (Formula presented.) particles per site are allowed. The process is constructed from a (Formula presented.)-dimensional representation of a quantum Hamiltonian with (Formula presented.) 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.
2016
5-nov-2015
166
3
887
933
A generalized asymmetric exclusion process with Uq(sl2) stochastic duality / Carinci, Gioia; Giardina', Cristian; Redig, Frank; Sasamoto, Tomohiro. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - 166:3(2016), pp. 887-933. [10.1007/s00440-015-0674-0]
Carinci, Gioia; Giardina', Cristian; Redig, Frank; Sasamoto, Tomohiro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1122135
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