论文标题
无序的晶格网络，跨越森林和布朗尼网络的传播和导航
Transmission and navigation on disordered lattice networks, directed spanning forests and Brownian web
论文作者
论文摘要
基于随机点集作为节点的随机网络引起了许多应用程序的极大兴趣，尤其是在通信网络中，包括无线传感器网络，点对点网络等。对此类网络的研究通常要求节点作为泊松点过程独立和均匀分布。在这项工作中，我们冒险超越了该标准范式，并研究了基于随机扰动的晶格，从\ textit {定向跨越森林}（DSF）获得的网络的随机几何形状，这些晶格具有所需的统计特性，这些统计特性是空间依赖点场的模型。在低疾病的状态下，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作为路径集合在扩散缩放下收敛到Brownian Web。
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 \textit{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.
