Lipschitz percolation

Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367, 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:	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:	06 May 2023 20:18
URI:	https://orca.cardiff.ac.uk/id/eprint/13074

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