论文标题
在几何环境中的社区检测和信息渗透
Community detection and percolation of information in a geometric setting
论文作者
论文摘要
在稀疏制度中，我们迈出了概括随机块模型理论的第一步，该模型将离散的社区结构被基本的几何形状取代。我们考虑在同质度量空间上的几何随机图，其中要连接两个顶点的概率是距离的任意函数。我们提供了足够的条件，在稀疏制度中，可以回收位置（最多是空间的同构）。此外，由于苔藓和佩雷斯，我们定义了在树上的信息流模型的几何对应物，其中人们考虑了在球体上的分支随机行走，目标是根据叶子的位置恢复根的位置。我们给出了一些足够的条件，可以在此模型中提供渗透和不变信息。
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph over a homogeneous metric space where the probability of two vertices to be connected is an arbitrary function of the distance. We give sufficient conditions under which the locations can be recovered (up to an isomorphism of the space) in the sparse regime. Moreover, we define a geometric counterpart of the model of flow of information on trees, due to Mossel and Peres, in which one considers a branching random walk on a sphere and the goal is to recover the location of the root based on the locations of leaves. We give some sufficient conditions for percolation and for non-percolation of information in this model.
