Max-linear models in random environment
将最大线性模型从有限有向无环图扩展到无限图和随机图，研究伯努利键渗流对模型的影响，发现定向方格图上的临界概率描述了相变，并讨论了在通信网络中的应用。
We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs as well as random graphs, and investigate their relations to classical percolation theory, more particularly the impact of Bernoulli bond percolation on such models. We show that the critical probability of percolation on the oriented square lattice graph Z2 describes a phase transition in the obtained model. Focus is on the dependence introduced by this graph into the max-linear model. We discuss natural applications in communication networks, in particular, concerning the propagation of influences.