Max-Linear Models on Infinite Graphs Generated by Bernoulli Bond Percolation

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Date
2018-05-17MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2018,09Author
Klüppelberg, Claudia
Sönmez, Ercan
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Show full item recordOWP-2018-09
Abstract
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 $\mathbb{Z}^2$ 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.