The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at equal time is known to converge to the Airy process or its variations. However, the temporal process, or more generally the two-dimensional space-time fluctuation field, is less well understood. We consider this question for the periodic TASEP (totally asymmetric simple exclusion process). For a particular initial condition, we evaluate the multi-time and multi-location distribution explicitly in terms of a multiple integral involving a Fredholm determinant. We then evaluate the large time limit in the so-called relaxation time scale.

中文翻译：

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周期性TASEP的多点分布

KPZ 类模型的高度波动预计会收敛到一个通用过程。已知相等时间的空间过程收敛于艾里过程或其变体。然而，时间过程，或者更普遍的二维时空波动场，还不太清楚。我们考虑周期性 TASEP（完全不对称的简单排除过程）的这个问题。对于特定的初始条件，我们根据涉及 Fredholm 行列式的多重积分明确评估多时间和多位置分布。然后我们在所谓的松弛时间尺度中评估大的时间限制。