Stochastic networks based on random point sets as nodes have attracted considerable interest in many applications, particularly in communication networks, including wireless sensor networks, peer-to-peer networks and so on. The study of such networks generally requires the nodes to be independently and uniformly distributed as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate the stochastic geometry of networks obtained from directed spanning forests (DSF) based on randomly perturbed lattices, which have desirable statistical properties as a models of spatially dependent point fields. In the regime of low disorder, we show in 2D and 3D that the DSF almost surely consists of a single tree. In 2D, we further establish that the DSF, as a collection of paths, converges under diffusive scaling to the Brownian web.

中文翻译：

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无序格网络、定向跨越森林和布朗网络上的传输和导航

基于随机点集作为节点的随机网络在许多应用中引起了相当大的兴趣，特别是在通信网络中，包括无线传感器网络、对等网络等。对此类网络的研究一般要求节点作为泊松点过程独立均匀分布。在这项工作中，我们冒险超越了这个标准范式，并研究了从基于随机扰动点阵的定向生成森林 (DSF) 获得的网络的随机几何形状，这些点阵具有理想的统计特性作为空间相关点场的模型。在低无序状态下，我们在 2D 和 3D 中表明 DSF 几乎肯定由一棵树组成。在 2D 中，我们进一步确定 DSF 作为路径的集合，