Lipschitz percolation

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

Lipschitz percolation

Probability 2009-11-25 v2

Authors: N. Dirr , P. W. Dondl , G. R. Grimmett , A. E. Holroyd , M. Scheutzow

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.

Keywords

percolation theory

Cite

@article{arxiv.0911.3384,
  title  = {Lipschitz percolation},
  author = {N. Dirr and P. W. Dondl and G. R. Grimmett and A. E. Holroyd and M. Scheutzow},
  journal= {arXiv preprint arXiv:0911.3384},
  year   = {2009}
}

Comments

Minor error corrected, and reference updated

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