Lipschitz percolation

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

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

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.
Original languageEnglish
Article numberPaper 2
Pages (from-to)14-21
Number of pages8
JournalElectronic Communications in Probability
Volume15
Publication statusPublished - 2010

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