论文标题
部分可观测时空混沌系统的无模型预测
Time-time covariance for last passage percolation in half-space
论文作者
论文摘要
本文研究了半个空间最后一段渗透的几种特性，尤其是两次协方差。我们表明，当两个端点处于较小的宏观距离时，对点对点模型的协方差的一阶校正与固定模型之一相同。为了获得结果，我们首先得出了不同模型的最后一段增量的比较不等式。这用于证明点对点过程的紧密度以及大地测量的本地化。与全空间情况不同，对于半个空间，我们必须克服难度，即在半空间中以通用的起点和终点为单位，尚不清楚。
This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-point process as well as localization of the geodesics. Unlike for the full-space case, for half-space we have to overcome the difficulty that the point-to-point model in half-space with generic start and end points is not known.
