ELECTRONIC COMMUNICATIONS in PROBABILITY

We prove the existence of a (random) Lipschitz function F : Z d 1 ! Z + such that, for every x2 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.