A driven tagged particle in asymmetric exclusion processes. (English) Zbl 1490.60284
Summary: We consider the asymmetric exclusion process with a driven tagged particle on \(\mathbb{Z}\) which has different jump rates from other particles. When the non-tagged particles have non-nearest-neighbor jump rates, we show that the tagged particle can have a speed which has a different sign from the mean derived from its jump rates. We also show the existence of some non-trivial invariant measures for the environment process viewed from the tagged particle. Our arguments are based on coupling, martingale methods, and analyzing currents through fixed bonds.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60F15 | Strong limit theorems |
| 60K37 | Processes in random environments |
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