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arXiv · 0911.3384

Lipschitz percolation

N. Dirr·P. W. Dondl·G. R. Grimmett·A. E. Holroyd·M. Scheutzow
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Abstract

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.

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N. Dirr, P. W. Dondl, G. R. Grimmett, A. E. Holroyd, M. Scheutzow. 2009-11-25. Lipschitz percolation. https://arxiv.org/abs/0911.3384

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