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Analysis and Stochastics Study Group: Lipschitz percolation
4 March 2015 13:00 in CM105
The following concept of Lipschitz percolation
was introduced in a joint paper with Dirr, Dondl, Grimmett and Holroyd in 2010: Consider Bernoulli site percolation in Zd+1
, i.e. each vertex in Zd+1
is open with probability p, independently for every vertex, where p ∈ (0,1) and d ∈ N are parameters. We say that Lipschitz percolation occurs, if there exists a (random) function F:Zd → Z whose graph only contains open sites and which satisfies |F(x)-F(y)| ≤ 1 whenever |x-y|=1. It has been shown that there exists a critical value pL(d) ∈ (0,1) such that for p>pL(d) Lipschitz percolation occurs with probability one while for p<pL(d) Lipschitz percolation will almost surely not occur. |
In this talk, which is based on joint work with Alex Drewitz and Maite Wilke Berenguer, we discuss the question of existence and upper and lower bounds for the critical value under the additional constraint that the graph of the function F lies above a tilted plane.
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