AI 中文总结
本文针对三维空间中节点位置服从高斯分布的N个移动设备随机网络，借助图拉普拉斯算子推导网络状态概率，得到小型网络、完全网络、孤立节点的连接概率结果并简化特殊情形。
AI 中文摘要
本文研究三维空间中N个移动设备构成的随机网络的连接性，每个设备（节点）在各维度上的位置服从高斯分布。对于每对节点，其连接概率与节点间距相关，由高斯连接函数描述。研究此类系统的基础分析工具是给定网络状态的概率，该概率可通过图拉普拉斯算子推导并表示。利用这一结果，我们得到了小型网络的连接性、完全网络（所有节点相互连接）的概率，以及孤立节点的概率，孤立节点概率可近似大型网络的连接概率。随后，将通用结果针对特殊情形和极限场景进行简化。
英文摘要
In this paper, we consider the connectivity of a random network of N mobile devices in three dimensions (3D), where the location of each device or node has a Gaussian distribution in each dimension. For each pair of nodes, the probability of connectivity is related to the nodes' separation by a Gaussian connectivity function. The fundamental analytical tool for studying such systems is the probability of a given network state, derived and expressed in terms of its graph Laplacian. Leveraging this result, we obtain results for the connectivity of small networks, the probability of a complete network (where all nodes are connected to all other nodes), and the probability of an isolated node, which gives an approximation to the connectivity probability of larger networks. The general results are then simplified for special cases and limiting scenarios.
CommentsAccepted to IEEE GLOBECOM 2026
