Claudia Klüppelberg, Ercan Sönmez
Published 2018-04-17Version 1
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.
On the Ornstein-Zernike behaviour for the Bernoulli bond percolation on $\mathbb{Z}^{d},d\geq3,$ in the supercitical regime
One-point boundaries of ends of clusters in percolation in $\mathbb H^d$
A remark on monotonicity in Bernoulli bond Percolation
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