Lipschitz percolation

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. © 2010 Applied Probability Trust.