论文标题
带有依赖和布朗网络的排水网络
A drainage network with dependence and the Brownian web
论文作者
论文摘要
我们研究了一个在整数晶格$ \ mathbb {z}^{d} $上进行合并的随机步行系统，其中步行在$ d $ theworker上定向并遵循某些指定的规则。我们首先研究了路径的几何形状，并表明，几乎可以肯定的是，仅由一棵树组成的一棵树组成的路径$ d = 2,3 $，以及无限的许多脱节树，用于尺寸$ d \ geq 4 $。同样，对于$ d \ geq 2 $，该图中没有Bi-Infinite路径。随后，我们证明，对于$ d = 2 $，该系统的扩散缩放比例收敛到布朗尼网络。
We study a system of coalescing random walks on the integer lattice $\mathbb{Z}^{d}$ in which the walk is oriented in the $d$-th direction and follows certain specified rules. We first study the geometry of the paths and show that, almost surely, the paths from a graph consisting of just one tree for dimentions $d=2,3$ and infinitely many disjoint trees for dimensions $d\geq 4$. Also, there is no bi-infinite path in the graph almost surely for $d\geq 2$. Subsequently, we prove that for $d=2$ the diffusive scaling of this system converges in distribution to the Brownian web.
