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Lipschitz percolation

Dirr, Nicolas P., Dondl, Patrick W., Grimmett, Geoffrey R., Holroyd, Alexander E. and Scheutzowv, Michael V. 2010. Lipschitz percolation. Electronic Communications in Probability 15 (2) , pp. 14-21.

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Percolation; Lipschitz embedding; Random surface
Additional Information: Pdf uploaded in accordance with publisher's policy at http://ecp.ejpecp.org/about/submissions#copyrightNotice (accessed 28/02/2014).
Publisher: Institute of Mathematical Statistics
ISSN: 1083-589X
Date of First Compliant Deposit: 30 March 2016
Last Modified: 04 Jun 2017 02:52
URI: http://orca.cf.ac.uk/id/eprint/13074

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