We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single Fredholm determinant representation for the joint distribution function of particle positions with arbitrary initial data. This formula is a generalization of the recent result by Mateski, Quastel and Remenik and allows us to take the KPZ scaling limit. For both the discrete time geometric and Bernoulli TASEPs, we show that the distribution functions converge to the one describing the KPZ fixed point.

中文翻译：

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离散时间TASEP的KPZ定点

我们考虑具有几何和伯努利跳跃概率的离散时间完全不对称简单排除过程（TASEP）的两种版本。对于混合了这些和连续时间动力学的过程，我们获得了具有任意初始数据的粒子位置联合分布函数的单个Fredholm行列式表示。该公式是对Mateski，Quastel和Remenik最近的结果的概括，它使我们可以采用KPZ缩放限制。对于离散时间几何和伯努利TASEP，我们表明分布函数收敛到描述KPZ不动点的那个。