Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Klüppelberg, ClaudiaSönmez, Ercan2024-10-162024-10-162018https://oa.tib.eu/renate/handle/123456789/16898https://doi.org/10.34657/15920We 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 Z² and nearest neighbor 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.eng510Bernoulli bond percolationExtreme value theoryGraphical modelInfinite graphPercolationRecursive max-linear modelReport