Report
Stationary States of the One-dimensional Facilitated Asymmetric Exclusion Process
| العنوان: | Stationary States of the One-dimensional Facilitated Asymmetric Exclusion Process |
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| المؤلفون: | Ayyer, A., Goldstein, S., Lebowitz, J. L., Speer, E. R. |
| المصدر: | Annales de l'Institut Henri Poincare - Probabilites et Statistiques 2023, Vol. 59, No. 2, 726--742 |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics Condensed Matter Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Probability, Condensed Matter - Statistical Mechanics, Mathematical Physics, 60K35 (Primary) 82C22, 82C23, 82C26 (Secondary) |
| الوصف: | We describe the translation invariant stationary states (TIS) of the one-dimensional facilitated asymmetric exclusion process in continuous time, in which a particle at site $i\in\mathbb{Z}$ jumps to site $i+1$ (respectively $i-1$) with rate $p$ (resp. $1-p$), provided that site $i-1$ (resp. $i+1$) is occupied and site $i+1$ (resp. $i-1$) is empty. All TIS states with density $\rho\le1/2$ are supported on trapped configurations in which no two adjacent sites are occupied; we prove that if in this case the initial state is i.i.d.~Bernoulli then the final state is independent of $p$. This independence also holds for the system on a finite ring. For $\rho>1/2$ there is only one TIS. It is the infinite volume limit of the probability distribution that gives uniform weight to all configurations in which no two holes are adjacent, and is isomorphic to the Gibbs measure for hard core particles with nearest neighbor exclusion. Comment: 32 pages, 4 figures. Version 2:Various revisions throughout; results unchanged. Version 3: date correction |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1214/22-AIHP1264 |
| URL الوصول: | http://arxiv.org/abs/2010.07257 |
| رقم الانضمام: | edsarx.2010.07257 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1214/22-AIHP1264 |
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