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2010 Lipschitz percolation
Nicolas Dirr, Patrick Dondl, Geoffrey Grimmett, Alexander Holroyd, Michael Scheutzow
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Electron. Commun. Probab. 15: 14-21 (2010). DOI: 10.1214/ECP.v15-1521


We prove the existence of a (random) Lipschitz function $F:\mathbb{Z}^{d-1}\to\mathbb{Z}^+$ such that, for every $x\in\mathbb{Z}^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\mathbb{Z}^{d}$. 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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Nicolas Dirr. Patrick Dondl. Geoffrey Grimmett. Alexander Holroyd. Michael Scheutzow. "Lipschitz percolation." Electron. Commun. Probab. 15 14 - 21, 2010.


Accepted: 21 January 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1193.60115
MathSciNet: MR2581044
Digital Object Identifier: 10.1214/ECP.v15-1521

Primary: 60K35
Secondary: 82B20

Keywords: Lipschitz embedding , percolation , Random surface

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