SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 65-93, January 2021.
The totally asymmetric simple exclusion process (TASEP) is a basic model of statistical mechanics that has found numerous applications. We consider the case of TASEP with a finite chain where particles may enter from the left and leave to the right at prescribed rates. This model can be formulated as a Markov process with a finite number of states. Due to the irreducibility of the process, it is well-known that the probability distribution on the states is globally attracted to a unique equilibrium distribution. We extend this result to the more detailed level of individual trajectories. To do so we formulate TASEP as a random dynamical system. Our main result is that the trajectories from all possible initial conditions contract to each other yielding the existence of a random attractor that consists of a single trajectory almost surely. This implies that in the long run TASEP “filters out” any perturbation that changes the state of the particles along the chain.

中文翻译：

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TASEP模型中的随机吸引

SIAM应用动力系统杂志，第20卷，第1期，第65-93页，2021年1月。
完全不对称的简单排除过程（TASEP）是统计力学的基本模型，已发现了许多应用。我们考虑具有有限链的TASEP的情况，其中粒子可能以规定的速率从左侧进入并离开右侧。该模型可以表示为具有有限状态数的马尔可夫过程。由于过程的不可约性，众所周知，状态的概率分布被全局吸引到唯一的平衡分布。我们将此结果扩展到单个轨迹的更详细的级别。为此，我们将TASEP公式化为随机动力学系统。我们的主要结果是，所有可能的初始条件下的轨迹彼此收缩，从而产生了几乎确定地由单个轨迹组成的随机吸引子。