Mathematics – Probability
Scientific paper
2009-11-17
Mathematics
Probability
Minor error corrected, and reference updated
Scientific paper
We prove the existence of a (random) Lipschitz function $F : \Z^{d-1}\to\Z^+$
such that, for every $x \in \Z^{d-1}$, the site $(x,F(x))$ is open in a site
percolation process on $\Z^{d}$. The Lipschitz constant may be taken to be 1
when the parameter $p$ of the percolation model is sufficiently close to 1.
Dirr Nicolas
Dondl Patrick W.
Grimmett Geoffrey R.
Holroyd Alexander E.
Scheutzow Michael
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