Periodic TASEP with general initial conditions
Periodic TASEP with general initial conditions
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DOI：
10.1007/s00440-020-01004-6
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发表时间：
2019-12
影响因子：
2
通讯作者：
J. Baik;Zhipeng Liu
中科院分区：
文献类型：
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作者：
J. Baik;Zhipeng Liu
考虑了空间周期域中具有任意初始条件的一维完全非对称简单排斥过程，得到了时空平面上多点分布的显式表达式.这些公式是用一个包含Fredholm行列式的积分给出的。然后，我们评估的大时间，大周期的限制，在弛豫时间尺度，这是规模，使系统的大小开始影响的高度波动。极限得到假设某些条件的初始条件，我们表明，步骤，平坦，和步骤平坦的初始条件满足。因此，我们得到了这三个初始条件在周期模型中的极限定理，推广了以前关于阶跃初始条件的工作。我们还考虑了均匀随机和均匀步长随机初始条件。
We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point distributions in the space-time plane. The formulas are given in terms of an integral involving a Fredholm determinant. We then evaluate the large-time, large-period limit in the relaxation time scale, which is the scale such that the system size starts to affect the height fluctuations. The limit is obtained assuming certain conditions on the initial condition, which we show that the step, flat, and step-flat initial conditions satisfy. Hence, we obtain the limit theorem for these three initial conditions in the periodic model, extending the previous work on the step initial condition. We also consider uniform random and uniform-step random initial conditions.