Max-linear models on infinite graphs generated by Bernoulli bond percolation
We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph Z^2 and nearest neighbour bond percolation. Focus is on the dependence introduced by this graph into the max-linear model. As a natural application, we consider communication networks, in particular, the distribution of extreme opinions in social networks.
Bernoulli bond percolation, extreme value theory, graphical model, infinite graph, percolation, recursive max-linear model.