Lipschitz percolation

Reference:

Dirr, N., Dondl, P. W., Grimmett, G. R., Holroyd, A. E. and Scheutzow, M., 2010. Lipschitz percolation. Electronic Communications in Probability, 15, Paper 2.

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Abstract

We prove the existence of a (random) Lipschitz function F : Z(d-1) -> Z(+) such that, for every x is an element of 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.

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