具有一般初始条件和确定性移动壁的TASEP
TASEP with a general initial condition and a deterministically moving wall
AI总结：
本文研究具有一般初始条件和确定性移动壁的TASEP，利用颜色-位置对称性将单点分布转化为阶跃初始条件TASEP的粒子位置问题，并分析了大时间渐近行为，揭示了壁影响区域边界处的新渐近现象及激波与乘积极限分布的关联。
摘要：
我们研究在$\mathbb{Z}$上具有一般初始条件和粒子前方确定性移动壁的完全非对称简单排他过程（TASEP）。利用颜色-位置对称性，我们将单点分布表示为具有阶跃初始条件的TASEP中沿类空路径的粒子位置。基于该公式，我们分析了模型在各种情形下的大时间渐近行为。对于阶跃初始条件以外的初始条件，我们在受壁影响区域的边界处识别出一种不同的渐近行为，这与[Borodin-Bufetov-Ferrari'24]和[Ferrari-Gernholt'24]中的观察结果不同。此外，我们证明了乘积极限分布与宏观经验密度中的激波相关联。作为我们起始公式的一个特例，我们推导出具有任意初始数据的TASEP单点分布的变分表达式。针对非随机初始条件（例如具有任意密度的周期初始条件），我们利用分析工具在粒子位置框架内刻画了极限分布。
英文摘要：
We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with a general initial condition and a deterministically moving wall in front of the particles. Using colour-position symmetry, we express the one-point distributions in terms of particle positions in a TASEP with step initial condition along a space-like path. Based on this formula, we analyse the large-time asymptotics of the model under various scenarios. For initial conditions other than the step initial condition, we identify a distinct asymptotic behaviour at the boundary of the region influenced by the wall, differing from the observations made in [Borodin-Bufetov-Ferrari'24] and [Ferrari-Gernholt'24]. Furthermore, we demonstrate that product limit distributions are associated with shocks in the macroscopic empirical density. As a special case of our starting formula, we derive a variational expression for the one-point distributions of TASEP with arbitrary initial data. Focusing on non-random initial conditions, such as periodic ones with an arbitrary density, we leverage our analytical tools to characterise the limit distribution within the framework of particle positions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
