Lipschitz percolation
Nicolas Dirr, University of Bath
Patrick W. Dondl, University of Bonn
Geoffrey R. Grimmett, Cambridge University
Alexander E. Holroyd, Microsoft Research; University of British Columbia
Michael Scheutzow, Technical University, Berlin
Abstract
We prove the existence of a (random) Lipschitz function
F: Zd-1 → Z+ such that,
for every x∈ Zd-1, the
site (x,F(x)) is open in a site percolation process on
Zd. The Lipschitz constant may be taken to be 1 when
the parameter p of the percolation model is sufficiently
close to 1.
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