The q-TASEP with a Random Initial Condition
The q-TASEP with a Random Initial Condition
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DOI：
10.1134/s0040577919010057
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发表时间：
2018-05
影响因子：
1
通讯作者：
T. Imamura;T. Sasamoto
中科院分区：
文献类型：
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作者：
T. Imamura;T. Sasamoto
研究一维Kardar-Parisi-Zhang模型（包括ASEP模型和q-TASEP模型）的涨落的标准方法是写出q-变形矩的公式并构造它们的母函数。这种方法适用于阶跃型的初始条件，但不适用于随机初始条件（包括平稳情况）：在这种情况下，只有前几个矩是有限的，其余的是发散的。我们以前提出了一种方法来克服这个困难，使用Ramanujan求和公式和柯西行列式的θ函数。在这里，我们提出了一种替代方法的q-TASEP不使用这些关系。
A standard approach for studying fluctuations of one-dimensional Kardar–Parisi–Zhang models, which include the ASEP and the q-TASEP, is to write a formula for the q-deformed moments and construct their generating function. This approach works well for an initial condition of the step type but not for a random initial condition (including the stationary case): in this case, only the first few moments are finite and the rest diverge. We previously presented a method for overcoming this difficulty using the Ramanujan summation formula and the Cauchy determinant for the theta functions. Here, we present an alternative approach for the q-TASEP without using these relations.