通过局部极限的级联存活核

中文摘要 AI 辅助

我们考虑标记网络上的一类一般级联过程，其中顶点根据局部顶点属性被迭代删除。在标记局部弱收敛下，我们建立了最终稳定集中顶点比例收敛到极限网络中存活概率的充分必要条件。在此条件下，我们还获得了由局部属性指定的子集中顶点比例的收敛性。

英文摘要

We consider a general class of cascading processes on marked networks, in which vertices are iteratively deleted according to a local vertex property. Under marked local-weak convergence, we establish a necessary and sufficient condition for the proportion of vertices in the final stable set to converge to the survival probability in the limiting network. Under this condition, we also obtain convergence of the proportions of vertices in subsets specified by local properties.

发表机构

• H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology（佐治亚理工学院 H. 米尔顿·斯图尔特工业与系统工程学院）
• Department of Mathematics, Aarhus University（奥胡斯大学数学系）
• California Institute of Technology（加州理工学院）

机构由 AI 辅助整理，请以论文原文为准。