论文标题
部分可观测时空混沌系统的无模型预测
The stationary horizon and semi-infinite geodesics in the directed landscape
论文作者
论文摘要
静止的地平线（SH）是一个随机过程的耦合布朗尼动作，其真实价值的漂移索引。它首先是由第一作者引入的，它是指数级上通用渗透过程的Busemann过程的扩散缩放限制。它是独立发现的，是第二和第三作者的Busemann过程。我们表明，在渐近空间斜率的条件下，SH是KPZ固定点的独特不变分布，也是KPZ固定点的吸引子。因此，Sh描述了定向景观的Busemann过程。这可以在所有初始点和方向上同时控制半无限大地测量学。 Busemann流程不连续的方向的可数密度集合$ξ$是一组方向，其中并非所有的大地测量学结合，并且每个初始点至少存在两个独特的大地测量学。这在每个$ξ$方向上创建了两个不同的聚集地球学系列。在$ξ$方向上，Busemann差异轮廓像布朗本地时代一样分布。我们描述了方向的点过程$ξ\inξ$和空间位置，其中$ξ\ pm $ busemann函数分开。
The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of the Busemann process of exponential last-passage percolation. It was independently discovered as the Busemann process of Brownian last-passage percolation by the second and third authors. We show that SH is the unique invariant distribution and an attractor of the KPZ fixed point under conditions on the asymptotic spatial slopes. It follows that SH describes the Busemann process of the directed landscape. This gives control of semi-infinite geodesics simultaneously across all initial points and directions. The countable dense set $Ξ$ of directions of discontinuity of the Busemann process is the set of directions in which not all geodesics coalesce and in which there exist at least two distinct geodesics from each initial point. This creates two distinct families of coalescing geodesics in each $Ξ$ direction. In $Ξ$ directions, the Busemann difference profile is distributed like Brownian local time. We describe the point process of directions $ξ\inΞ$ and spatial locations where the $ξ\pm$ Busemann functions separate.
