Max-linear models in random environment

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 Z(2) 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. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

We extend the previous work on max-linear models on finite directed acyclic graphs to infinite and random graphs. We investigate their connections with classical percolation theory, specifically focusing on the impact of Bernoulli bond percolation on these models. Our study reveals that the critical probability of percolation on the oriented square lattice graph Z(2) describes a phase transition in the obtained model. We discuss the significance of this graph-induced dependence in max-linear models and its applications in communication networks, particularly in influence propagation.