论文标题
随机块模型上的引导性渗透
Bootstrap percolation on the stochastic block model
论文作者
论文摘要
我们分析了随机块模型（SBM）上的引导程序渗透过程，这是ERDőS-Rényi随机图的自然扩展，该图包含在许多实际系统中观察到的社区结构。在SBM中，节点分为两个子集，这些子集代表不同的社区，并且成对的节点与取决于其所属社区的概率独立相关。在对系统参数的轻度假设下，我们证明了最终数量的活性节点数量的尖锐相变的存在，并根据最初有效的节点的数量来表征亚临界和超临界状态，这些节点的数量在每个社区中随机选择。
We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erdős--Rényi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are partitioned into two subsets, which represent different communities, and pairs of nodes are independently connected with a probability that depends on the communities they belong to. Under mild assumptions on the system parameters, we prove the existence of a sharp phase transition for the final number of active nodes and characterize the sub-critical and the super-critical regimes in terms of the number of initially active nodes, which are selected uniformly at random in each community.
