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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Analysis and Stochastics Study Group: Lipschitz percolation

Presented by Michael Scheutzow, TU Berlin

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 dN are parameters. We say that Lipschitz percolation occurs, if there exists a (random) function F:ZdZ 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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