The KPZ fixed point for discrete time TASEPs
The KPZ fixed point for discrete time TASEPs
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DOI：
10.1088/1751-8121/aba213
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发表时间：
2020-10-16
影响因子：
2.1
通讯作者：
Arai, Yuta
中科院分区：
文献类型：
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作者：
Arai, Yuta
我们考虑两个版本的离散时间完全不对称简单排斥过程（TASEPs）的几何和伯努利跳跃概率。对于混合这些和连续时间动力学的过程，我们得到一个单一的Fredholm行列式表示的联合分布函数的粒子位置与任意初始数据。这个公式是Mateski，Quastel和Remenik最近的结果的推广，并允许我们采取KPZ标度极限。对于离散时间几何和Bernoulli TASEPs，我们证明了分布函数收敛到描述KPZ不动点的分布函数。
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.