论文标题
eNaud-derrida的矩阵产品ANSATZ代表的间隔的KPZ方程的固定度量
Stationary measures of the KPZ equation on an interval from Enaud-Derrida's matrix product ansatz representation
论文作者
论文摘要
最近已经计算出Kardar-Parisi-Zhang方程的固定度量。我们通过将基质产物ANSATZ的弱不对称限制用于不对称的简单排除过程来提出这一结果的直接推导。我们依靠Enaud和Derrida的矩阵产品ANSATZ表示，这允许以重新加权的简单随机步行来表达稳态。在连续限制中，其度量成为liouville量子力学中遇到的形式的路径积分（或重新加权的布朗运动），从而恢复了最近的公式。
The stationary measures of the Kardar-Parisi-Zhang equation on an interval have been computed recently. We present a rather direct derivation of this result by taking the weak asymmetry limit of the matrix product ansatz for the asymmetric simple exclusion process. We rely on the matrix product ansatz representation of Enaud and Derrida, which allows to express the steady-state in terms of re-weighted simple random walks. In the continuum limit, its measure becomes a path integral (or re-weighted Brownian motion) of the form encountered in Liouville quantum mechanics, recovering the recent formula.
