Spatial correlations of the 1D KPZ surface on a flat substrate
Spatial correlations of the 1D KPZ surface on a flat substrate
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DOI：
10.1088/0305-4470/38/33/l01
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发表时间：
2005-08-19
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影响因子：
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通讯作者：
Sasamoto, T
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文献类型：
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作者：
Sasamoto, T
我们研究了一维KPZ曲面在平坦初始条件下的空间关联。结果表明，高程的多点联合分布由一个Fredholm型行列式给出，其核在标度极限中被显式得到。这也可以描述GOE Dyson布朗运动模型中最大本征值的动力学。我们的分析是基于一个恶性行走问题的完全ASEP的行列式格林函数的重新表述。
We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm determinant, with its kernel in the scaling limit explicitly obtained. This may also describe the dynamics of the largest eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a reformulation of the determinantal Green's function for the totally ASEP in terms of a vicious walk problem.