TY - JOUR
T1 - Asymmetric Stochastic Transport Models with Uq(su(1,1)) Symmetry
AU - Carinci, G
AU - Giardina', Cristian
AU - Redig, FHJ
AU - Sasamoto, Tomohiro
PY - 2016
Y1 - 2016
N2 - By using the algebraic construction outlined in Carinci et al. (arXiv:1407.3367, 2014), we introduce several Markov processes related to the Uq(su(1,1)) quantum Lie algebra. These processes serve as asymmetric transport models and their algebraic structure easily allows to deduce duality properties of the systems. The results include: (a) the asymmetric version of the Inclusion Process, which is self-dual; (b) the diffusion limit of this process, which is a natural asymmetric analogue of the and which turns out to have the Symmetric Inclusion Process as a dual process; (c) the asymmetric analogue of the KMP Process, which also turns out to have a symmetric dual process. We give applications of the various duality relations by computing exponential moments of the current.
AB - By using the algebraic construction outlined in Carinci et al. (arXiv:1407.3367, 2014), we introduce several Markov processes related to the Uq(su(1,1)) quantum Lie algebra. These processes serve as asymmetric transport models and their algebraic structure easily allows to deduce duality properties of the systems. The results include: (a) the asymmetric version of the Inclusion Process, which is self-dual; (b) the diffusion limit of this process, which is a natural asymmetric analogue of the and which turns out to have the Symmetric Inclusion Process as a dual process; (c) the asymmetric analogue of the KMP Process, which also turns out to have a symmetric dual process. We give applications of the various duality relations by computing exponential moments of the current.
UR - http://resolver.tudelft.nl/uuid:6ad12bd5-7c4a-4706-b856-bc036b7492a8
U2 - 10.1007/s10955-016-1473-4
DO - 10.1007/s10955-016-1473-4
M3 - Article
SN - 0022-4715
VL - 163
SP - 239
EP - 279
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 2
ER -